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Complete non-self-adjacent paths:Results 02B
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a = 15, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 132 38
8 164 60
9 400 114
10 620 192
11 1128 342
12 1696 564
13 2912 956
14 4604 1584
15 7796 2686
16 12556 4524
17 20732 7680
18 33156 12850
19 52868 21144
20 75952 31026
21 108396 45368
22 110712 45502
23 133976 56920
24 96332 40262
25 87276 37550
26 51860 22582
27 31500 14008
28 14928 6838
29 6264 2926
30 1968 966
31 552 276
32 40 20
Total 858620 357016
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
L
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 0 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 0 0 0 0 9 0 0 0
0 0 0 0 4 0 0 0 0 0 4 0 0 0 0
0 0 0 9 0 0 0 0 0 0 0 9 0 0 0
7 1 1 1 0 13 0 0 0 0 0 13 0 1 1 1
2 2 4 8 4 8 4 4 4 8 4 8 4 2 2
1 1 1 0 13 0 0 0 0 0 13 0 1 1 1
8 0 0 0 3 0 17 0 0 0 17 0 3 0 0 0
2 2 2 4 18 4 8 4 8 4 18 4 2 2 2
0 0 0 3 0 17 0 0 0 17 0 3 0 0 0
9 3 3 4 4 14 4 25 4 25 4 14 4 4 3 3
4 4 4 6 8 40 8 16 8 40 8 6 4 4 4
3 3 4 4 14 4 25 4 25 4 14 4 4 3 3
10 4 4 4 9 8 36 8 58 8 36 8 9 4 4 4
4 4 4 4 8 8 70 8 70 8 8 4 4 4 4
4 4 4 9 8 36 8 58 8 36 8 9 4 4 4
11 9 10 11 10 22 18 111 18 111 18 22 10 11 10 9
6 6 6 6 8 22 12 196 12 22 8 6 6 6 6
9 10 11 10 22 18 111 18 111 18 22 10 11 10 9
12 12 12 12 17 12 67 24 276 24 67 12 17 12 12 12
10 10 10 10 14 16 180 20 180 16 14 10 10 10 10
12 12 12 17 12 67 24 276 24 67 12 17 12 12 12
13 21 22 24 23 71 28 293 44 293 28 71 23 24 22 21
20 20 20 24 20 206 36 204 36 206 20 24 20 20 20
21 22 24 23 71 28 293 44 293 28 71 23 24 22 21
14 32 33 33 79 34 412 46 216 46 412 34 79 33 33 32
36 36 40 36 278 36 254 64 254 36 278 36 40 36 36
32 33 33 79 34 412 46 216 46 412 34 79 33 33 32
15 57 62 109 64 623 70 308 78 308 70 623 64 109 62 57
62 66 62 370 62 524 60 56 60 524 62 370 62 66 62
57 62 109 64 623 70 308 78 308 70 623 64 109 62 57
16 96 152 104 903 105 597 84 198 84 597 105 903 104 152 96
106 102 484 102 1008 98 88 20 88 98 1008 102 484 102 106
96 152 104 903 105 597 84 198 84 597 105 903 104 152 96
17 220 180 1292 186 1233 161 272 52 272 161 1233 186 1292 180 220
168 632 168 1794 164 262 36 4 36 262 164 1794 168 632 168
220 180 1292 186 1233 161 272 52 272 161 1233 186 1292 180 220
18 280 1789 304 2393 270 487 58 194 58 487 270 2393 304 1789 280
834 280 3002 276 718 100 12 0 12 100 718 276 3002 280 834
280 1789 304 2393 270 487 58 194 58 487 270 2393 304 1789 280
19 2433 502 4417 480 1044 136 266 58 266 136 1044 480 4417 502 2433
474 4784 470 1800 238 52 2 0 2 52 238 1800 470 4784 474
2433 502 4417 480 1044 136 266 58 266 136 1044 480 4417 502 2433
20 792 7712 812 2278 289 463 57 196 57 463 289 2278 812 7712 792
7328 802 4136 506 188 14 0 0 0 14 188 506 4136 802 7328
792 7712 812 2278 289 463 57 196 57 463 289 2278 812 7712 792
21 12787 1374 4992 648 964 120 270 58 270 120 964 648 4992 1374 12787
1364 8790 996 614 64 2 0 0 0 2 64 614 996 8790 1364
12787 1374 4992 648 964 120 270 58 270 120 964 648 4992 1374 12787
22 2204 10582 1328 2016 225 467 58 196 58 467 225 2016 1328 10582 2204
17454 1860 1846 224 16 0 0 0 0 0 16 224 1846 1860 17454
2204 10582 1328 2016 225 467 58 196 58 467 225 2016 1328 10582 2204
23 20165 2570 4267 488 961 124 269 58 269 124 961 488 4267 2570 20165
3358 5140 658 84 2 0 0 0 0 0 2 84 658 5140 3358
20165 2570 4267 488 961 124 269 58 269 124 961 488 4267 2570 20165
24 4496 8087 1040 1934 225 467 58 196 58 467 225 1934 1040 8087 4496
13288 1698 352 18 0 0 0 0 0 0 0 18 352 1698 13288
4496 8087 1040 1934 225 467 58 196 58 467 225 1934 1040 8087 4496
25 11929 2136 3280 458 921 119 268 56 268 119 921 458 3280 2136 11929
3972 1286 100 2 0 0 0 0 0 0 0 2 100 1286 3972
11929 2136 3280 458 921 119 268 56 268 119 921 458 3280 2136 11929
26 3796 3825 820 1382 209 431 57 196 57 431 209 1382 820 3825 3796
4254 420 20 0 0 0 0 0 0 0 0 0 20 420 4254
3796 3825 820 1382 209 431 57 196 57 431 209 1382 820 3825 3796
27 3225 1174 1375 380 557 106 237 54 237 106 557 380 1375 1174 3225
1462 124 2 0 0 0 0 0 0 0 0 0 2 124 1462
3225 1174 1375 380 557 106 237 54 237 106 557 380 1375 1174 3225
28 1060 940 464 458 162 213 50 152 50 213 162 458 464 940 1060
596 22 0 0 0 0 0 0 0 0 0 0 0 22 596
1060 940 464 458 162 213 50 152 50 213 162 458 464 940 1060
29 383 318 276 167 154 76 97 44 97 76 154 167 276 318 383
144 2 0 0 0 0 0 0 0 0 0 0 0 2 144
383 318 276 167 154 76 97 44 97 76 154 167 276 318 383
30 84 101 80 71 49 45 32 36 32 45 49 71 80 101 84
24 0 0 0 0 0 0 0 0 0 0 0 0 0 24
84 101 80 71 49 45 32 36 32 45 49 71 80 101 84
31 14 22 21 18 17 18 18 18 18 18 17 18 21 22 14
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
14 22 21 18 17 18 18 18 18 18 17 18 21 22 14
32 0 1 1 1 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 1 1 1 0
Total 64104 41614 25076 14479 8184 4684 2968 2458 2968 4684 8184 14479 25076 41614 64104
54974 26096 12390 5892 2822 1392 770 596 770 1392 2822 5892 12390 26096 54974
64104 41614 25076 14479 8184 4684 2968 2458 2968 4684 8184 14479 25076 41614 64104
Grand total = 596 + 2*770 + 2*1392 + 2*2822 + 2*5892 + 2*12390 + 2*26096 + 2*54974 + 2*2458 + 4*2968 + 4*4684 + 4*8184 + 4*14479 + 4*25076 + 4*41614 + 4*64104
= 858620
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 12 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 12 12 12 12 11 7 5 90
11 158 9 14 17 23 24 24 24 24 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 24 24 24 24 23 17 14 9 158
12 265 11 17 22 25 33 34 34 34 33 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 33 34 34 34 33 25 22 17 11 265
13 445 21 31 36 46 53 63 64 63 53 46 36 31 21 445
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
445 21 31 36 46 53 63 64 63 53 46 36 31 21 445
14 741 34 46 55 60 76 89 100 89 76 60 55 46 34 741
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
741 34 46 55 60 76 89 100 89 76 60 55 46 34 741
15 1248 63 85 95 107 120 151 158 151 120 107 95 85 63 1248
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
1248 63 85 95 107 120 151 158 151 120 107 95 85 63 1248
16 2107 104 139 154 163 180 185 214 185 180 163 154 139 104 2107
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2107 104 139 154 163 180 185 214 185 180 163 154 139 104 2107
17 3569 177 241 263 279 276 273 208 273 276 279 263 241 177 3569
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
3569 177 241 263 279 276 273 208 273 276 279 263 241 177 3569
18 5980 290 395 432 427 392 247 252 247 392 427 432 395 290 5980
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5980 290 395 432 427 392 247 252 247 392 427 432 395 290 5980
19 9813 489 666 708 664 428 335 226 335 428 664 708 666 489 9813
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
9813 489 666 708 664 428 335 226 335 428 664 708 666 489 9813
20 14247 821 1088 1105 771 558 271 254 271 558 771 1105 1088 821 14247
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14247 821 1088 1105 771 558 271 254 271 558 771 1105 1088 821 14247
21 20557 1370 1749 1407 1067 493 343 224 343 493 1067 1407 1749 1370 20557
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
20557 1370 1749 1407 1067 493 343 224 343 493 1067 1407 1749 1370 20557
22 19309 2201 2319 1944 926 586 267 252 267 586 926 1944 2319 2201 19309
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19309 2201 2319 1944 926 586 267 252 267 586 926 1944 2319 2201 19309
23 23561 2906 3235 1718 1144 486 334 218 334 486 1144 1718 3235 2906 23561
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
23561 2906 3235 1718 1144 486 334 218 334 486 1144 1718 3235 2906 23561
24 13559 3921 2721 2082 871 553 255 242 255 553 871 2082 2721 3921 13559
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13559 3921 2721 2082 871 553 255 242 255 553 871 2082 2721 3921 13559
25 12568 2830 3179 1422 984 423 311 202 311 423 984 1422 3179 2830 12568
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
12568 2830 3179 1422 984 423 311 202 311 423 984 1422 3179 2830 12568
26 5353 3091 1701 1442 603 449 216 220 216 449 603 1442 1701 3091 5353
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5353 3091 1701 1442 603 449 216 220 216 449 603 1442 1701 3091 5353
27 3147 1396 1477 678 590 263 242 162 242 263 590 678 1477 1396 3147
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
3147 1396 1477 678 590 263 242 162 242 263 590 678 1477 1396 3147
28 1037 939 583 500 247 231 118 154 118 231 247 500 583 939 1037
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1037 939 583 500 247 231 118 154 118 231 247 500 583 939 1037
29 346 330 293 190 164 100 108 68 108 100 164 190 293 330 346
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
346 330 293 190 164 100 108 68 108 100 164 190 293 330 346
30 75 103 83 72 53 50 36 40 36 50 53 72 83 103 75
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
75 103 83 72 53 50 36 40 36 50 53 72 83 103 75
31 13 22 21 18 18 18 18 18 18 18 18 18 21 22 13
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
13 22 21 18 18 18 18 18 18 18 18 18 21 22 13
32 0 1 1 1 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 1 1 1 0
Total 138313 21141 20102 14384 9258 5818 3946 3360 3946 5818 9258 14384 20102 21141 138313
26 0 0 0 0 0 0 0 0 0 0 0 0 0 26
138313 21141 20102 14384 9258 5818 3946 3360 3946 5818 9258 14384 20102 21141 138313
Grand total = 2*26 + 2*3360 + 4*3946 + 4*5818 + 4*9258 + 4*14384 + 4*20102 + 4*21141 + 4*138313
= 858620
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
L
3 2 1 0 0 0 0 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 0 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 0 0 0 0 9 5 7 11
12 22 18 12 4 0 0 0 0 0 4 12 18 22 12
11 7 5 9 0 0 0 0 0 0 0 9 5 7 11
7 25 24 23 21 23 10 10 10 10 10 23 21 23 24 25
26 38 40 32 20 12 8 8 8 12 20 32 40 38 26
25 24 23 21 23 10 10 10 10 10 23 21 23 24 25
8 32 27 24 31 28 27 10 10 10 27 28 31 24 27 32
36 62 50 48 46 24 16 12 16 24 46 48 50 62 36
32 27 24 31 28 27 10 10 10 27 28 31 24 27 32
9 68 67 72 93 92 76 71 50 71 76 92 93 72 67 68
76 118 96 104 100 96 56 52 56 96 100 104 96 118 76
68 67 72 93 92 76 71 50 71 76 92 93 72 67 68
10 108 100 99 135 156 154 112 128 112 154 156 135 99 100 108
120 208 176 158 182 180 166 108 166 180 182 158 176 208 120
108 100 99 135 156 154 112 128 112 154 156 135 99 100 108
11 201 191 194 252 302 314 337 264 337 314 302 252 194 191 201
218 358 308 284 304 352 338 392 338 352 304 284 308 358 218
201 191 194 252 302 314 337 264 337 314 302 252 194 191 201
12 320 289 280 367 422 508 531 680 531 508 422 367 280 289 320
346 590 508 466 478 542 748 768 748 542 478 466 508 590 346
320 289 280 367 422 508 531 680 531 508 422 367 280 289 320
13 557 518 513 661 807 910 1230 1222 1230 910 807 661 513 518 557
600 992 856 806 822 1102 1344 1584 1344 1102 822 806 856 992 600
557 518 513 661 807 910 1230 1222 1230 910 807 661 513 518 557
14 910 842 816 1094 1264 1804 1944 2116 1944 1804 1264 1094 816 842 910
984 1656 1418 1352 1646 1964 2470 2548 2470 1964 1646 1352 1418 1656 984
910 842 816 1094 1264 1804 1944 2116 1944 1804 1264 1094 816 842 910
15 1566 1485 1517 1950 2817 3074 3587 3676 3587 3074 2817 1950 1517 1485 1566
1696 2828 2424 2612 3056 3930 4132 4248 4132 3930 3056 2612 2424 2828 1696
1566 1485 1517 1950 2817 3074 3587 3676 3587 3074 2817 1950 1517 1485 1566
16 2618 2517 2510 4041 4549 5487 5683 5816 5683 5487 4549 4041 2510 2517 2618
2844 4786 4472 4672 6096 6688 6906 6716 6906 6688 6096 4672 4472 4786 2844
2618 2517 2510 4041 4549 5487 5683 5816 5683 5487 4549 4041 2510 2517 2618
17 4523 4327 5472 6834 8882 9260 9380 9242 9380 9260 8882 6834 5472 4327 4523
4852 8586 7964 9608 10496 11344 11174 11200 11174 11344 10496 9608 7964 8586 4852
4523 4327 5472 6834 8882 9260 9380 9242 9380 9260 8882 6834 5472 4327 4523
18 7500 8655 8927 13487 14558 14910 14450 14382 14450 14910 14558 13487 8927 8655 7500
8632 14782 16074 16612 17938 17866 18072 18144 18072 17866 17938 16612 16074 14782 8632
7500 8655 8927 13487 14558 14910 14450 14382 14450 14910 14558 13487 8927 8655 7500
19 14347 14270 19015 22286 24034 23516 23019 22596 23019 23516 24034 22286 19015 14270 14347
14312 28308 27490 28806 27978 28364 28864 29108 28864 28364 27978 28806 27490 28308 14312
14347 14270 19015 22286 24034 23516 23019 22596 23019 23516 24034 22286 19015 14270 14347
20 19655 28020 29138 35012 35327 34422 33037 32778 33037 34422 35327 35012 29138 28020 19655
26688 43224 43502 40132 39898 40782 41986 42616 41986 40782 39898 40132 43502 43224 26688
19655 28020 29138 35012 35327 34422 33037 32778 33037 34422 35327 35012 29138 28020 19655
21 40304 41640 46838 51068 51220 49077 48021 47446 48021 49077 51220 51068 46838 41640 40304
39460 70382 61750 57598 56626 58724 59894 59884 59894 58724 56626 57598 61750 70382 39460
40304 41640 46838 51068 51220 49077 48021 47446 48021 49077 51220 51068 46838 41640 40304
22 36879 53608 55181 57463 54217 52313 51296 51506 51296 52313 54217 57463 55181 53608 36879
51102 66592 59680 55646 59374 61596 60486 59872 60486 61596 59374 55646 59680 66592 51102
36879 53608 55181 57463 54217 52313 51296 51506 51296 52313 54217 57463 55181 53608 36879
23 62760 68460 70391 69569 67256 64232 63832 63616 63832 64232 67256 69569 70391 68460 62760
64606 88012 69486 67026 71884 73864 73194 72072 73194 73864 71884 67026 69486 88012 64606
62760 68460 70391 69569 67256 64232 63832 63616 63832 64232 67256 69569 70391 68460 62760
24 46757 59871 56558 53993 49484 48135 47423 47716 47423 48135 49484 53993 56558 59871 46757
56220 50310 46280 48586 51946 52544 51832 52216 51832 52544 51946 48586 46280 50310 56220
46757 59871 56558 53993 49484 48135 47423 47716 47423 48135 49484 53993 56558 59871 46757
25 50429 55535 55646 50407 47725 45269 45529 45296 45529 45269 47725 50407 55646 55535 50429
53402 47212 37804 41954 47586 46700 46700 46432 46700 46700 47586 41954 37804 47212 53402
50429 55535 55646 50407 47725 45269 45529 45296 45529 45269 47725 50407 55646 55535 50429
26 33783 38581 34513 31815 28578 28243 27556 27760 27556 28243 28578 31815 34513 38581 33783
36648 20924 21224 25702 26792 27712 27388 27784 27388 27712 26792 25702 21224 20924 36648
33783 38581 34513 31815 28578 28243 27556 27760 27556 28243 28578 31815 34513 38581 33783
27 22679 24127 23382 20055 19016 17808 18075 17670 18075 17808 19016 20055 23382 24127 22679
23704 11226 11140 14260 16544 15668 16550 16408 16550 15668 16544 14260 11140 11226 23704
22679 24127 23382 20055 19016 17808 18075 17670 18075 17808 19016 20055 23382 24127 22679
28 12007 12619 11364 10212 9141 9137 8727 8932 8727 9137 9141 10212 11364 12619 12007
12398 3690 4800 6796 6998 7606 7432 7852 7432 7606 6998 6796 4800 3690 12398
12007 12619 11364 10212 9141 9137 8727 8932 8727 9137 9141 10212 11364 12619 12007
29 5438 5534 5186 4515 4255 4019 4084 3892 4084 4019 4255 4515 5186 5534 5438
5530 1046 1694 2458 2778 2796 3128 2888 3128 2796 2778 2458 1694 1046 5530
5438 5534 5186 4515 4255 4019 4084 3892 4084 4019 4255 4515 5186 5534 5438
30 1870 1815 1694 1525 1403 1392 1326 1352 1326 1392 1403 1525 1694 1815 1870
1884 136 456 692 740 876 864 940 864 876 740 692 456 136 1884
1870 1815 1694 1525 1403 1392 1326 1352 1326 1392 1403 1525 1694 1815 1870
31 548 527 509 467 452 442 436 434 436 442 452 467 509 527 548
550 4 84 120 152 172 184 188 184 172 152 120 84 4 550
548 527 509 467 452 442 436 434 436 442 452 467 509 527 548
32 40 40 38 36 36 36 36 36 36 36 36 36 38 40 40
40 0 4 8 8 8 8 8 8 8 8 8 4 0 40
40 40 38 36 36 36 36 36 36 36 36 36 38 40 40
Total 365950 423708 429910 437398 426044 414575 409742 408626 409742 414575 426044 437398 429910 423708 365950
407000 466120 419812 426554 450492 461512 463940 464048 463940 461512 450492 426554 419812 466120 407000
365950 423708 429910 437398 426044 414575 409742 408626 409742 414575 426044 437398 429910 423708 365950
Grand total = 4*365950 + 2*407000 + 2*408626 + 4*409742 + 4*414575 + 2*419812 + 4*423708 + 4*426044 + 2*426554 + 4*429910 + 4*437398 + 2*450492 + 2*461512 + 2*463940 + 464048 + 2*466120
= 19101468
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44
EN
0 0 0 26 50 74 100 182 374 756 1442 2630 4662 8054 13360 20586 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398 17694 14 2 4 17 50 112 228
424 760 1382 2544 4616 8078 13428 20680
1 0 0 0 13 3 13 22 63 131 235 400 693 1207 2025 3134 13 0 1 1 1 3 7 15 31 65 137 289 609 1283 2703 0 0 0 0 11 31 42
55 97 197 392 725 1257 2067 3170
2 24 0 0 0 24 6 24 40 112 230 408 684 1152 1910 2952 12 12 0 2 2 2 6 14 30 62 130 274 578 1218 2566 0 0 0 0 0 20 56
76 100 174 344 664 1188 1974 3032
3 33 33 0 0 0 33 9 33 54 147 297 519 852 1377 2109 11 11 11 0 3 3 3 9 21 45 93 195 411 867 1827 11 0 0 0 0 0 27
75 102 135 231 441 816 1389 2151
4 40 30 40 0 0 0 40 12 40 64 168 332 568 904 1368 30 10 10 10 0 4 4 4 12 28 60 124 260 548 1156 40 20 0 0 0 0 0
32 88 120 160 268 488 848 1328
5 54 45 27 45 0 0 0 45 15 45 70 175 335 555 840 63 27 9 9 9 0 5 5 5 15 35 75 155 325 685 90 63 27 0 0 0 0
0 35 95 130 175 285 485 760
6 112 64 48 24 48 0 0 0 48 18 48 72 168 306 480 120 56 24 8 8 8 0 6 6 6 18 42 90 186 390 160 112 80 32 0 0 0
0 0 36 96 132 180 282 432
7 245 147 70 49 21 49 0 0 0 49 21 49 70 147 245 217 105 49 21 7 7 7 0 7 7 7 21 49 105 217 259 175 126 91 35 0 0
0 0 0 35 91 126 175 259
8 480 306 168 72 48 18 48 0 0 0 48 24 48 64 112 390 186 90 42 18 6 6 6 0 8 8 8 24 56 120 432 282 180 132 96 36 0
0 0 0 0 32 80 112 160
9 840 555 335 175 70 45 15 45 0 0 0 45 27 45 54 685 325 155 75 35 15 5 5 5 0 9 9 9 27 63 760 485 285 175 130 95 35
0 0 0 0 0 27 63 90
10 1368 904 568 332 168 64 40 12 40 0 0 0 40 30 40 1156 548 260 124 60 28 12 4 4 4 0 10 10 10 30 1328 848 488 268 160 120 88
32 0 0 0 0 0 20 40
11 2109 1377 852 519 297 147 54 33 9 33 0 0 0 33 33 1827 867 411 195 93 45 21 9 3 3 3 0 11 11 11 2151 1389 816 441 231 135 102
75 27 0 0 0 0 0 11
12 2952 1910 1152 684 408 230 112 40 24 6 24 0 0 0 24 2566 1218 578 274 130 62 30 14 6 2 2 2 0 12 12 3032 1974 1188 664 344 174 100
76 56 20 0 0 0 0 0
13 3134 2025 1207 693 400 235 131 63 22 13 3 13 0 0 0 2703 1283 609 289 137 65 31 15 7 3 1 1 1 0 13 3170 2067 1257 725 392 197 97
55 42 31 11 0 0 0 0
14 20586 13360 8054 4662 2630 1442 756 374 182 100 74 50 26 0 0 17694 8398 3986 1892 898 426 202 96 46 22 10 4 2 2 0 20680 13428 8078 4616 2544 1382 760
424 228 112 50 17 4 2 14
15 0 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0
0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 13 0
30 14 2 4 17 50 112 228 424 760 1382 2544 4616 8078 13428 20680 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398 17694 0 0 26 50 74 100 182
374 756 1442 2630 4662 8054 13360 20586
31 0 0 0 0 11 31 42 55 97 197 392 725 1257 2067 3170 13 0 1 1 1 3 7 15 31 65 137 289 609 1283 2703 0 0 0 13 3 13 22
63 131 235 400 693 1207 2025 3134
32 0 0 0 0 0 20 56 76 100 174 344 664 1188 1974 3032 12 12 0 2 2 2 6 14 30 62 130 274 578 1218 2566 24 0 0 0 24 6 24
40 112 230 408 684 1152 1910 2952
33 11 0 0 0 0 0 27 75 102 135 231 441 816 1389 2151 11 11 11 0 3 3 3 9 21 45 93 195 411 867 1827 33 33 0 0 0 33 9
33 54 147 297 519 852 1377 2109
34 40 20 0 0 0 0 0 32 88 120 160 268 488 848 1328 30 10 10 10 0 4 4 4 12 28 60 124 260 548 1156 40 30 40 0 0 0 40
12 40 64 168 332 568 904 1368
35 90 63 27 0 0 0 0 0 35 95 130 175 285 485 760 63 27 9 9 9 0 5 5 5 15 35 75 155 325 685 54 45 27 45 0 0 0
45 15 45 70 175 335 555 840
36 160 112 80 32 0 0 0 0 0 36 96 132 180 282 432 120 56 24 8 8 8 0 6 6 6 18 42 90 186 390 112 64 48 24 48 0 0
0 48 18 48 72 168 306 480
37 259 175 126 91 35 0 0 0 0 0 35 91 126 175 259 217 105 49 21 7 7 7 0 7 7 7 21 49 105 217 245 147 70 49 21 49 0
0 0 49 21 49 70 147 245
38 432 282 180 132 96 36 0 0 0 0 0 32 80 112 160 390 186 90 42 18 6 6 6 0 8 8 8 24 56 120 480 306 168 72 48 18 48
0 0 0 48 24 48 64 112
39 760 485 285 175 130 95 35 0 0 0 0 0 27 63 90 685 325 155 75 35 15 5 5 5 0 9 9 9 27 63 840 555 335 175 70 45 15
45 0 0 0 45 27 45 54
40 1328 848 488 268 160 120 88 32 0 0 0 0 0 20 40 1156 548 260 124 60 28 12 4 4 4 0 10 10 10 30 1368 904 568 332 168 64 40
12 40 0 0 0 40 30 40
41 2151 1389 816 441 231 135 102 75 27 0 0 0 0 0 11 1827 867 411 195 93 45 21 9 3 3 3 0 11 11 11 2109 1377 852 519 297 147 54
33 9 33 0 0 0 33 33
42 3032 1974 1188 664 344 174 100 76 56 20 0 0 0 0 0 2566 1218 578 274 130 62 30 14 6 2 2 2 0 12 12 2952 1910 1152 684 408 230 112
40 24 6 24 0 0 0 24
43 3170 2067 1257 725 392 197 97 55 42 31 11 0 0 0 0 2703 1283 609 289 137 65 31 15 7 3 1 1 1 0 13 3134 2025 1207 693 400 235 131
63 22 13 3 13 0 0 0
44 20680 13428 8078 4616 2544 1382 760 424 228 112 50 17 4 2 14 17694 8398 3986 1892 898 426 202 96 46 22 10 4 2 2 0 20586 13360 8054 4662 2630 1442 756
374 182 100 74 50 26 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*10 + 1*14 + 1*17 + 1*22 + 1*26 + 1*46 + 2*50 + 1*74 + 1*96 + 1*100 + 1*112 + 1*182 + 1*202 + 1*228 + 1*374 + 1*424 + 1*426 + 1*756 + 1*760 + 1*898 + 1*1382 + 1*1442 +
1*1892 + 1*2544 + 1*2630 + 1*3986 + 1*4616 + 1*4662 + 1*8054 + 1*8078 + 1*8398 + 1*13360 + 1*13428 + 1*17694 + 1*20586 + 1*20680)
4(8*0 + 3*1 + 2*3 + 1*7 + 1*11 + 3*13 + 1*15 + 1*22 + 2*31 + 1*42 + 1*55 + 1*63 + 1*65 + 1*97 + 1*131 + 1*137 + 1*197 + 1*235 + 1*289 + 1*392 + 1*400 + 1*609 + 1*693 + 1*725 + 1*1207 + 1*1257 +
1*1283 + 1*2025 + 1*2067 + 1*2703 + 1*3134 + 1*3170)
4(9*0 + 3*2 + 2*6 + 2*12 + 1*14 + 1*20 + 3*24 + 1*30 + 1*40 + 1*56 + 1*62 + 1*76 + 1*100 + 1*112 + 1*130 + 1*174 + 1*230 + 1*274 + 1*344 + 1*408 + 1*578 + 1*664 + 1*684 + 1*1152 + 1*1188 +
1*1218 + 1*1910 + 1*1974 + 1*2566 + 1*3032 + 1*2952)
4(9*0 + 3*3 + 2*9 + 4*11 + 1*21 + 1*27 + 4*33 + 1*45 + 1*54 + 1*75 + 1*93 + 1*102 + 1*135 + 1*147 + 1*195 + 1*231 + 1*297 + 1*411 + 1*441 + 1*519 + 1*816 + 1*852 + 1*867 + 1*1377 + 1*1389 +
1*1827 + 1*2109 + 1*2151)
4(9*0 + 3*4 + 3*10 + 2*12 + 1*20 + 1*28 + 2*30 + 1*32 + 5*40 + 1*60 + 1*64 + 1*88 + 1*120 + 1*124 + 1*160 + 1*168 + 1*260 + 1*268 + 1*332 + 1*488 + 1*548 + 1*568 + 1*848 + 1*904 + 1*1156 +
1*1328 + 1*1368)
4(9*0 + 3*5 + 3*9 + 2*15 + 3*27 + 2*35 + 4*45 + 1*54 + 2*63 + 1*70 + 1*75 + 1*90 + 1*95 + 1*130 + 1*155 + 2*175 + 1*285 + 1*325 + 1*335 + 1*485 + 1*555 + 1*685 + 1*760 + 1*840)
4(9*0 + 3*6 + 3*8 + 2*18 + 2*24 + 1*32 + 1*36 + 1*42 + 4*48 + 1*56 + 1*64 + 1*72 + 1*80 + 1*90 + 1*96 + 2*112 + 1*120 + 1*132 + 1*160 + 1*168 + 1*180 + 1*186 + 1*282 + 1*306 + 1*390 + 1*432 +
1*480)
2(9*0 + 6*7 + 4*21 + 2*35 + 6*49 + 2*70 + 2*91 + 2*105 + 2*126 + 2*147 + 2*175 + 2*217 + 2*245 + 2*259)
2(43*0 + 2*13) +
13(45*0)
= 553252 + 84564 + 80408 + 57536 + 37032 + 23272 + 15784 + 6720 + 52
= 858620
Value repetition frequencies = 4(35*1 + 2*2 + 2*3) +
4(27*1 + 2*2 + 2*3 + 1*8) +
4(26*1 + 2*2 + 2*3 + 1*9) +
4(23*1 + 1*2 + 1*3 + 2*4 + 1*9) +
4(21*1 + 2*2 + 2*3 + 1*5 + 1*9) +
4(15*1 + 4*2 + 3*3 + 1*4 + 1*9) +
4(20*1 + 3*2 + 2*3 + 1*4 + 1*9) +
2(10*2 + 1*4 + 2*6 + 1*9) +
2(1*2 + 1*43) +
13(1*45)
= 2025
Number of distinct row element sets = 10
Number of rows = 2*2 + 7*4 + 1*13
= 45
Number of distinct values = 175
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 20 21
Frequency 913 12 24 20 20 12 20 16 12 20 16 20 16 16 8 12 4 8 8 12
Distinct values 22 24 26 27 28 30 31 32 33 35 36 40 42 45 46 48 49 50 54 55
Frequency 8 20 4 16 4 12 8 8 16 12 4 24 8 20 4 16 12 8 8 4
Distinct values 56 60 62 63 64 65 70 72 74 75 76 80 88 90 91 93 95 96 97 100
Frequency 8 4 4 12 8 4 8 4 4 8 4 4 4 8 4 4 4 8 4 8
Distinct values 102 105 112 120 124 126 130 131 132 135 137 147 155 160 168 174 175 180 182 186
Frequency 4 4 16 8 4 4 8 4 4 4 4 8 4 8 8 4 12 4 4 4
Distinct values 195 197 202 217 228 230 231 235 245 259 260 268 274 282 285 289 297 306 325 332
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 335 344 374 390 392 400 408 411 424 426 432 441 480 485 488 519 548 555 568 578
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 609 664 684 685 693 725 756 760 816 840 848 852 867 898 904 1152 1156 1188 1207 1218
Frequency 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 1257 1283 1328 1368 1377 1382 1389 1442 1827 1892 1910 1974 2025 2067 2109 2151 2544 2566 2630 2703
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 2952 3032 3134 3170 3986 4616 4662 8054 8078 8398 13360 13428 17694 20586 20680
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 125*4 + 22*8 + 10*12 + 8*16 + 7*20 + 2*24 + 1*913
= 2025
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 22*36 + 4*37 + 4*42
= 1112
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 868
Number of possible SN-EN pairs with SN != EN = 44*45
= 1980
a = 16, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 136 38
8 168 60
9 416 114
10 644 192
11 1176 342
12 1764 564
13 3040 956
14 4808 1584
15 8172 2686
16 13176 4524
17 21820 7684
18 35164 12964
19 57204 21796
20 91092 36064
21 136220 55028
22 198832 82678
23 221908 91090
24 278776 118340
25 216536 89768
26 213576 91564
27 133760 57426
28 90740 39980
29 47100 21112
30 21852 10092
31 8492 3998
32 2512 1236
33 648 324
34 44 22
Total 1809876 752264
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
L
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 0 0 0 0 0 9 0 0 0
0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 0
0 0 0 9 0 0 0 0 0 0 0 0 9 0 0 0
7 1 1 1 0 13 0 0 0 0 0 0 13 0 1 1 1
2 2 4 8 4 8 4 4 4 4 8 4 8 4 2 2
1 1 1 0 13 0 0 0 0 0 0 13 0 1 1 1
8 0 0 0 3 0 17 0 0 0 0 17 0 3 0 0 0
2 2 2 4 18 4 8 4 4 8 4 18 4 2 2 2
0 0 0 3 0 17 0 0 0 0 17 0 3 0 0 0
9 3 3 4 4 14 4 25 4 4 25 4 14 4 4 3 3
4 4 4 6 8 40 8 12 12 8 40 8 6 4 4 4
3 3 4 4 14 4 25 4 4 25 4 14 4 4 3 3
10 4 4 4 9 8 36 8 33 33 8 36 8 9 4 4 4
4 4 4 4 8 8 66 12 12 66 8 8 4 4 4 4
4 4 4 9 8 36 8 33 33 8 36 8 9 4 4 4
11 9 10 11 10 22 18 82 47 47 82 18 22 10 11 10 9
6 6 6 6 8 18 16 104 104 16 18 8 6 6 6 6
9 10 11 10 22 18 82 47 47 82 18 22 10 11 10 9
12 12 12 12 17 12 34 57 150 150 57 34 12 17 12 12 12
10 10 10 10 10 20 46 154 154 46 20 10 10 10 10 10
12 12 12 17 12 34 57 150 150 57 34 12 17 12 12 12
13 21 22 24 23 34 65 71 266 266 71 65 34 23 24 22 21
20 20 20 20 24 22 220 122 122 220 22 24 20 20 20 20
21 22 24 23 34 65 71 266 266 71 65 34 23 24 22 21
14 32 33 33 38 75 52 406 141 141 406 52 75 38 33 33 32
36 36 36 40 36 278 44 278 278 44 278 36 40 36 36 36
32 33 33 38 75 52 406 141 141 406 52 75 38 33 33 32
15 57 62 64 109 75 618 111 299 299 111 618 75 109 64 62 57
62 62 66 62 370 62 526 86 86 526 62 370 62 66 62 62
57 62 64 109 75 618 111 299 299 111 618 75 109 64 62 57
16 96 103 153 109 899 124 585 175 175 585 124 899 109 153 103 96
102 106 102 484 102 1008 98 98 98 98 1008 102 484 102 106 102
96 103 153 109 899 124 585 175 175 585 124 899 109 153 103 96
17 167 233 186 1292 198 1228 204 248 248 204 1228 198 1292 186 233 167
172 168 632 168 1794 164 262 38 38 262 164 1794 168 632 168 172
167 233 186 1292 198 1228 204 248 248 204 1228 198 1292 186 233 167
18 337 297 1796 310 2389 289 476 146 146 476 289 2389 310 1796 297 337
280 834 280 3002 276 718 100 12 12 100 718 276 3002 280 834 280
337 297 1796 310 2389 289 476 146 146 476 289 2389 310 1796 297 337
19 473 2462 516 4421 492 1040 179 245 245 179 1040 492 4421 516 2462 473
1126 474 4784 470 1800 238 52 2 2 52 238 1800 470 4784 474 1126
473 2462 516 4421 492 1040 179 245 245 179 1040 492 4421 516 2462 473
20 3310 839 7729 824 2275 308 452 146 146 452 308 2275 824 7729 839 3310
806 7328 802 4136 506 188 14 0 0 14 188 506 4136 802 7328 806
3310 839 7729 824 2275 308 452 146 146 452 308 2275 824 7729 839 3310
21 1337 12921 1404 5004 664 960 164 249 249 164 960 664 5004 1404 12921 1337
10874 1364 8790 996 614 64 2 0 0 2 64 614 996 8790 1364 10874
1337 12921 1404 5004 664 960 164 249 249 164 960 664 5004 1404 12921 1337
22 20614 2349 10674 1350 2019 245 456 147 147 456 245 2019 1350 10674 2349 20614
2308 17454 1860 1846 224 16 0 0 0 0 16 224 1846 1860 17454 2308
20614 2349 10674 1350 2019 245 456 147 147 456 245 2019 1350 10674 2349 20614
23 3761 21865 2656 4336 512 961 168 249 249 168 961 512 4336 2656 21865 3761
32696 3358 5140 658 84 2 0 0 0 0 2 84 658 5140 3358 32696
3761 21865 2656 4336 512 961 168 249 249 168 961 512 4336 2656 21865 3761
24 40906 4911 9301 1092 1984 251 457 147 147 457 251 1984 1092 9301 4911 40906
5934 13288 1698 352 18 0 0 0 0 0 0 18 352 1698 13288 5934
40906 4911 9301 1092 1984 251 457 147 147 457 251 1984 1092 9301 4911 40906
25 8395 18660 2386 4125 498 962 167 248 248 167 962 498 4125 2386 18660 8395
32026 3972 1286 100 2 0 0 0 0 0 0 2 100 1286 3972 32026
8395 18660 2386 4125 498 962 167 248 248 167 962 498 4125 2386 18660 8395
26 30510 4917 7552 970 1944 245 456 147 147 456 245 1944 970 7552 4917 30510
8612 4254 420 20 0 0 0 0 0 0 0 0 20 420 4254 8612
30510 4917 7552 970 1944 245 456 147 147 456 245 1944 970 7552 4917 30510
27 8953 10268 1828 3309 476 916 162 246 246 162 916 476 3309 1828 10268 8953
12976 1462 124 2 0 0 0 0 0 0 0 0 2 124 1462 12976
8953 10268 1828 3309 476 916 162 246 246 162 916 476 3309 1828 10268 8953
28 10354 2947 3845 844 1379 228 420 146 146 420 228 1379 844 3845 2947 10354
4426 596 22 0 0 0 0 0 0 0 0 0 0 22 596 4426
10354 2947 3845 844 1379 228 420 146 146 420 228 1379 844 3845 2947 10354
29 3485 3098 1212 1382 391 552 148 215 215 148 552 391 1382 1212 3098 3485
2438 144 2 0 0 0 0 0 0 0 0 0 0 2 144 2438
3485 3098 1212 1382 391 552 148 215 215 148 552 391 1382 1212 3098 3485
30 1662 1045 968 470 454 181 202 117 117 202 181 454 470 968 1045 1662
704 24 0 0 0 0 0 0 0 0 0 0 0 0 24 704
1662 1045 968 470 454 181 202 117 117 202 181 454 470 968 1045 1662
31 449 469 328 275 178 148 101 88 88 101 148 178 275 328 469 449
172 2 0 0 0 0 0 0 0 0 0 0 0 0 2 172
449 469 328 275 178 148 101 88 88 101 148 178 275 328 469 449
32 99 119 102 85 67 55 46 42 42 46 55 67 85 102 119 99
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 26
99 119 102 85 67 55 46 42 42 46 55 67 85 102 119 99
33 15 24 23 20 19 20 20 20 20 20 20 19 20 23 24 15
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
15 24 23 20 19 20 20 20 20 20 20 19 20 23 24 15
34 0 1 1 1 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 1 1 1 0
Total 135063 87677 52818 30441 17093 9559 5625 3963 3963 5625 9559 17093 30441 52818 87677 135063
115826 54978 26098 12398 5910 2858 1466 926 926 1466 2858 5910 12398 26098 54978 115826
135063 87677 52818 30441 17093 9559 5625 3963 3963 5625 9559 17093 30441 52818 87677 135063
Grand total = 2*926 + 2*1466 + 2*2858 + 4*3963 + 4*5625 + 2*5910 + 4*9559 + 2*12398 + 4*17093 + 2*26098 + 4*30441 + 4*52818 + 2*54978 + 4*87677 + 2*115826 + 4*135063
= 1809876
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 12 12 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 12 12 12 12 12 11 7 5 90
11 158 9 14 17 23 24 24 24 24 24 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 24 24 24 24 24 23 17 14 9 158
12 265 11 17 22 25 33 34 34 34 34 33 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 33 34 34 34 34 33 25 22 17 11 265
13 445 21 31 36 46 53 63 64 64 63 53 46 36 31 21 445
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
445 21 31 36 46 53 63 64 64 63 53 46 36 31 21 445
14 741 34 46 55 60 76 89 101 101 89 76 60 55 46 34 741
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
741 34 46 55 60 76 89 101 101 89 76 60 55 46 34 741
15 1248 63 85 95 107 120 152 172 172 152 120 107 95 85 63 1248
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
1248 63 85 95 107 120 152 172 172 152 120 107 95 85 63 1248
16 2107 104 139 154 163 181 201 245 245 201 181 163 154 139 104 2107
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2107 104 139 154 163 181 201 245 245 201 181 163 154 139 104 2107
17 3571 177 241 263 280 294 316 312 312 316 294 280 263 241 177 3571
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
3571 177 241 263 280 294 316 312 312 316 294 280 263 241 177 3571
18 6037 290 395 433 447 449 415 325 325 415 449 447 433 395 290 6037
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6037 290 395 433 447 449 415 325 325 415 449 447 433 395 290 6037
19 10139 489 667 730 737 684 470 384 384 470 684 737 730 667 489 10139
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
10139 489 667 730 737 684 470 384 384 470 684 737 730 667 489 10139
20 16765 822 1112 1196 1143 799 585 351 351 585 799 1143 1196 1112 822 16765
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16765 822 1112 1196 1143 799 585 351 351 585 799 1143 1196 1112 822 16765
21 25360 1396 1860 1927 1478 1099 540 394 394 540 1099 1478 1927 1860 1396 25360
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
25360 1396 1860 1927 1478 1099 540 394 394 540 1099 1478 1927 1860 1396 25360
22 37740 2333 3023 2613 2052 977 619 351 351 619 977 2052 2613 3023 2333 37740
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37740 2333 3023 2613 2052 977 619 351 351 619 977 2052 2613 3023 2333 37740
23 39611 3808 4277 3724 1903 1218 545 390 390 545 1218 1903 3724 4277 3808 39611
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
39611 3808 4277 3724 1903 1218 545 390 390 545 1218 1903 3724 4277 3808 39611
24 50375 5353 6123 3522 2375 992 609 345 345 609 992 2375 3522 6123 5353 50375
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
50375 5353 6123 3522 2375 992 609 345 345 609 992 2375 3522 6123 5353 50375
25 32462 7524 5737 4440 1896 1171 524 379 379 524 1171 1896 4440 5737 7524 32462
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
32462 7524 5737 4440 1896 1171 524 379 379 524 1171 1896 4440 5737 7524 32462
26 32877 6333 7013 3226 2153 889 574 329 329 574 889 2153 3226 7013 6333 32877
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32877 6333 7013 3226 2153 889 574 329 329 574 889 2153 3226 7013 6333 32877
27 15129 7378 4227 3452 1448 995 459 351 351 459 995 1448 3452 4227 7378 15129
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
15129 7378 4227 3452 1448 995 459 351 351 459 995 1448 3452 4227 7378 15129
28 10377 3675 4031 1786 1447 619 466 284 284 466 619 1447 1786 4031 3675 10377
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10377 3675 4031 1786 1447 619 466 284 284 466 619 1447 1786 4031 3675 10377
29 3748 2952 1727 1498 686 599 294 270 270 294 599 686 1498 1727 2952 3748
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
3748 2952 1727 1498 686 599 294 270 270 294 599 686 1498 1727 2952 3748
30 1539 1125 1043 588 503 259 242 164 164 242 259 503 588 1043 1125 1539
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1539 1125 1043 588 503 259 242 164 164 242 259 503 588 1043 1125 1539
31 407 476 353 294 196 168 120 108 108 120 168 196 294 353 476 407
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
407 476 353 294 196 168 120 108 108 120 168 196 294 353 476 407
32 89 121 105 86 71 60 50 46 46 50 60 71 86 105 121 89
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
89 121 105 86 71 60 50 46 46 50 60 71 86 105 121 89
33 14 24 23 20 20 20 20 20 20 20 20 20 20 23 24 14
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
14 24 23 20 20 20 20 20 20 20 20 20 20 23 24 14
34 0 1 1 1 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 1 1 1 0
Total 291419 44531 42308 30201 19285 11805 7437 5469 5469 7437 11805 19285 30201 42308 44531 291419
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28
291419 44531 42308 30201 19285 11805 7437 5469 5469 7437 11805 19285 30201 42308 44531 291419
Grand total = 2*28 + 4*5469 + 4*7437 + 4*11805 + 4*19285 + 4*30201 + 4*42308 + 4*44531 + 4*291419
= 1809876
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
L
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 0 0 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 0 0 0 0 0 9 5 7 11
12 22 18 12 4 0 0 0 0 0 0 4 12 18 22 12
11 7 5 9 0 0 0 0 0 0 0 0 9 5 7 11
7 25 24 23 21 23 10 10 10 10 10 10 23 21 23 24 25
26 38 40 32 20 12 8 8 8 8 12 20 32 40 38 26
25 24 23 21 23 10 10 10 10 10 10 23 21 23 24 25
8 32 27 24 31 28 27 10 10 10 10 27 28 31 24 27 32
36 62 50 48 46 24 16 12 12 16 24 46 48 50 62 36
32 27 24 31 28 27 10 10 10 10 27 28 31 24 27 32
9 68 67 72 93 92 76 71 50 50 71 76 92 93 72 67 68
76 118 96 104 100 96 56 48 48 56 96 100 104 96 118 76
68 67 72 93 92 76 71 50 50 71 76 92 93 72 67 68
10 108 100 99 135 156 154 112 103 103 112 154 156 135 99 100 108
120 208 176 158 182 180 162 100 100 162 180 182 158 176 208 120
108 100 99 135 156 154 112 103 103 112 154 156 135 99 100 108
11 201 191 194 252 302 314 308 251 251 308 314 302 252 194 191 201
218 358 308 284 304 348 330 292 292 330 348 304 284 308 358 218
201 191 194 252 302 314 308 251 251 308 314 302 252 194 191 201
12 320 289 280 367 422 475 514 524 524 514 475 422 367 280 289 320
346 590 508 466 474 534 606 678 678 606 534 474 466 508 590 346
320 289 280 367 422 475 514 524 524 514 475 422 367 280 289 320
13 557 518 513 661 770 889 970 1211 1211 970 889 770 661 513 518 557
600 992 856 802 814 910 1194 1414 1414 1194 910 814 802 856 992 600
557 518 513 661 770 889 970 1211 1211 970 889 770 661 513 518 557
14 910 842 816 1053 1239 1398 1919 2027 2027 1919 1398 1239 1053 816 842 910
984 1656 1414 1344 1396 1738 2112 2604 2604 2112 1738 1396 1344 1414 1656 984
910 842 816 1053 1239 1398 1919 2027 2027 1919 1398 1239 1053 816 842 910
15 1566 1485 1472 1921 2215 3017 3326 3775 3775 3326 3017 2215 1921 1472 1485 1566
1696 2824 2416 2296 2738 3244 4124 4398 4398 4124 3244 2738 2296 2416 2824 1696
1566 1485 1472 1921 2215 3017 3326 3775 3775 3326 3017 2215 1921 1472 1485 1566
16 2618 2468 2477 3185 4434 4856 5789 6114 6114 5789 4856 4434 3185 2477 2468 2618
2840 4778 4082 4246 4874 6508 7000 7198 7198 7000 6508 4874 4246 4082 4778 2840
2618 2468 2477 3185 4434 4856 5789 6114 6114 5789 4856 4434 3185 2477 2468 2618
17 4472 4291 4296 6627 7535 9356 9781 9966 9966 9781 9356 7535 6627 4296 4291 4472
4850 8122 7422 7566 9956 11198 11994 11714 11714 11994 11198 9956 7566 7422 8122 4850
4472 4291 4296 6627 7535 9356 9781 9966 9966 9781 9356 7535 6627 4296 4291 4472
18 7569 7164 8636 10912 14662 15381 15661 15430 15430 15661 15381 14662 10912 8636 7164 7569
8144 14230 12946 15524 17252 19272 19134 19144 19144 19134 19272 17252 15524 12946 14230 8144
7569 7164 8636 10912 14662 15381 15661 15430 15430 15661 15381 14662 10912 8636 7164 7569
19 12717 14059 14476 22525 24545 25663 25117 24764 24764 25117 25663 24545 22525 14476 14059 12717
14366 24442 26120 27340 30536 30640 31058 31204 31204 31058 30640 30536 27340 26120 24442 14366
12717 14059 14476 22525 24545 25663 25117 24764 24764 25117 25663 24545 22525 14476 14059 12717
20 23547 23188 31199 36937 40944 40540 39589 38663 38663 39589 40540 40944 36937 31199 23188 23547
23846 46558 45260 48942 48296 49082 49440 50282 50282 49440 49082 48296 48942 45260 46558 23846
23547 23188 31199 36937 40944 40540 39589 38663 38663 39589 40540 40944 36937 31199 23188 23547
21 34125 47245 49052 61268 62846 61689 59387 58436 58436 59387 61689 62846 61268 49052 47245 34125
44952 74108 76362 71928 72006 72714 74612 75532 75532 74612 72714 72006 71928 76362 74108 44952
34125 47245 49052 61268 62846 61689 59387 58436 58436 59387 61689 62846 61268 49052 47245 34125
22 69677 71419 82895 91854 92989 89298 87214 86134 86134 87214 89298 92989 91854 82895 71419 69677
68038 125390 112670 106966 104242 107654 109558 109674 109674 109558 107654 104242 106966 112670 125390 68038
69677 71419 82895 91854 92989 89298 87214 86134 86134 87214 89298 92989 91854 82895 71419 69677
23 69225 101336 105113 112452 107457 103615 101265 101358 101358 101265 103615 107457 112452 105113 101336 69225
96764 133488 122190 112370 117958 122896 122282 120352 120352 122282 122896 117958 112370 122190 133488 96764
69225 101336 105113 112452 107457 103615 101265 101358 101358 101265 103615 107457 112452 105113 101336 69225
24 124509 134169 139852 141295 137461 131246 129757 129608 129608 129757 131246 137461 141295 139852 134169 124509
126688 185204 149296 141332 148358 153802 153620 151218 151218 153620 153802 148358 141332 149296 185204 126688
124509 134169 139852 141295 137461 131246 129757 129608 129608 129757 131246 137461 141295 139852 134169 124509
25 95760 126857 122675 119315 110131 106729 105123 105363 105363 105123 106729 110131 119315 122675 126857 95760
119328 118292 107018 108794 116912 118464 116710 117276 117276 116710 118464 116912 108794 107018 118292 119328
95760 126857 122675 119315 110131 106729 105123 105363 105363 105123 106729 110131 119315 122675 126857 95760
26 116685 128679 129508 119813 113846 108263 108239 108010 108010 108239 108263 113846 119813 129508 128679 116685
123028 123898 97616 103942 116396 115650 114968 114904 114904 114968 115650 116396 103942 97616 123898 123028
116685 128679 129508 119813 113846 108263 108239 108010 108010 108239 108263 113846 119813 129508 128679 116685
27 80980 95090 85990 79918 72241 70932 69530 69488 69488 69530 70932 72241 79918 85990 95090 80980
89814 58574 57612 66788 70058 71706 71148 71722 71722 71148 71706 70058 66788 57612 58574 89814
80980 95090 85990 79918 72241 70932 69530 69488 69488 69530 70932 72241 79918 85990 95090 80980
28 61335 65950 64557 55968 52938 49807 50171 49487 49487 50171 49807 52938 55968 64557 65950 61335
64514 37748 34216 42054 48672 46604 47930 48196 48196 47930 46604 48672 42054 34216 37748 64514
61335 65950 64557 55968 52938 49807 50171 49487 49487 50171 49807 52938 55968 64557 65950 61335
29 35445 38281 34438 31207 27934 27769 26811 26835 26835 26811 27769 27934 31207 34438 38281 35445
37066 14156 16480 22048 22782 24268 24026 24684 24684 24026 24268 22782 22048 16480 14156 37066
35445 38281 34438 31207 27934 27769 26811 26835 26835 26811 27769 27934 31207 34438 38281 35445
30 18017 18489 17408 14983 14093 13278 13342 13011 13011 13342 13278 14093 14983 17408 18489 18017
18482 4942 6610 9276 10524 10360 11274 11070 11070 11274 10360 10524 9276 6610 4942 18482
18017 18489 17408 14983 14093 13278 13342 13011 13011 13342 13278 14093 14983 17408 18489 18017
31 7520 7636 7052 6305 5789 5675 5492 5452 5452 5492 5675 5789 6305 7052 7636 7520
7628 1222 2194 3262 3498 3892 3984 4104 4104 3984 3892 3498 3262 2194 1222 7628
7520 7636 7052 6305 5789 5675 5492 5452 5452 5492 5675 5789 6305 7052 7636 7520
32 2405 2331 2196 1975 1845 1800 1744 1728 1728 1744 1800 1845 1975 2196 2331 2405
2420 148 544 820 912 1052 1100 1148 1148 1100 1052 912 820 544 148 2420
2405 2331 2196 1975 1845 1800 1744 1728 1728 1744 1800 1845 1975 2196 2331 2405
33 644 621 601 555 538 526 518 514 514 518 526 538 555 601 621 644
646 4 92 132 168 192 208 216 216 208 192 168 132 92 4 646
644 621 601 555 538 526 518 514 514 518 526 538 555 601 621 644
34 44 44 42 40 40 40 40 40 40 40 40 40 40 42 44 44
44 0 4 8 8 8 8 8 8 8 8 8 8 4 0 44
44 44 42 40 40 40 40 40 40 40 40 40 40 42 44 44
Total 771107 892879 905966 921677 897515 872823 861810 858362 858362 861810 872823 897515 921677 905966 892879 771107
857586 982200 884630 898888 949486 973048 978662 979200 979200 978662 973048 949486 898888 884630 982200 857586
771107 892879 905966 921677 897515 872823 861810 858362 858362 861810 872823 897515 921677 905966 892879 771107
Grand total = 4*771107 + 2*857586 + 4*858362 + 4*861810 + 4*872823 + 2*884630 + 4*892879 + 4*897515 + 2*898888 + 4*905966 + 4*921677 + 2*949486 + 2*973048 + 2*978662 + 2*979200 + 2*982200
= 42935956
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47
EN
0 0 0 28 54 80 108 198 412 844 1632 3024 5474 9748 16936 28162 43416 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398 17694 37280 15 2 4 18 54
122 250 468 846 1558 2920 5426 9802 17054 28278 43528
1 0 0 0 14 3 14 24 70 147 266 458 810 1459 2574 4308 6650 14 0 1 1 1 3 7 15 31 65 137 289 609 1283 2703 5695 0 0 0 0 12
34 46 60 107 222 452 856 1527 2618 4314 6632
2 26 0 0 0 26 6 26 44 126 262 470 800 1386 2414 4050 6268 13 13 0 2 2 2 6 14 30 62 130 274 578 1218 2566 5406 0 0 0 0 0
22 62 84 110 194 394 784 1450 2514 4134 6340
3 36 36 0 0 0 36 9 36 60 168 345 612 1026 1728 2865 4428 12 12 12 0 3 3 3 9 21 45 93 195 411 867 1827 3849 12 0 0 0 0
0 30 84 114 150 261 516 996 1782 2961 4548
4 44 33 44 0 0 0 44 12 44 72 196 396 692 1136 1836 2812 33 11 11 11 0 4 4 4 12 28 60 124 260 548 1156 2436 44 22 0 0 0
0 0 36 100 136 180 308 588 1088 1852 2868
5 60 50 30 50 0 0 0 50 15 50 80 210 415 710 1130 1710 70 30 10 10 10 0 5 5 5 15 35 75 155 325 685 1445 100 70 30 0 0
0 0 0 40 110 150 200 335 610 1060 1660
6 126 72 54 27 54 0 0 0 54 18 54 84 210 402 666 1008 135 63 27 9 9 9 0 6 6 6 18 42 90 186 390 822 180 126 90 36 0
0 0 0 0 42 114 156 210 342 582 912
7 280 168 80 56 24 56 0 0 0 56 21 56 84 196 357 560 248 120 56 24 8 8 8 0 7 7 7 21 49 105 217 455 296 200 144 104 40
0 0 0 0 0 42 112 154 210 329 504
8 560 357 196 84 56 21 56 0 0 0 56 24 56 80 168 280 455 217 105 49 21 7 7 7 0 8 8 8 24 56 120 248 504 329 210 154 112
42 0 0 0 0 0 40 104 144 200 296
9 1008 666 402 210 84 54 18 54 0 0 0 54 27 54 72 126 822 390 186 90 42 18 6 6 6 0 9 9 9 27 63 135 912 582 342 210 156
114 42 0 0 0 0 0 36 90 126 180
10 1710 1130 710 415 210 80 50 15 50 0 0 0 50 30 50 60 1445 685 325 155 75 35 15 5 5 5 0 10 10 10 30 70 1660 1060 610 335 200
150 110 40 0 0 0 0 0 30 70 100
11 2812 1836 1136 692 396 196 72 44 12 44 0 0 0 44 33 44 2436 1156 548 260 124 60 28 12 4 4 4 0 11 11 11 33 2868 1852 1088 588 308
180 136 100 36 0 0 0 0 0 22 44
12 4428 2865 1728 1026 612 345 168 60 36 9 36 0 0 0 36 36 3849 1827 867 411 195 93 45 21 9 3 3 3 0 12 12 12 4548 2961 1782 996 516
261 150 114 84 30 0 0 0 0 0 12
13 6268 4050 2414 1386 800 470 262 126 44 26 6 26 0 0 0 26 5406 2566 1218 578 274 130 62 30 14 6 2 2 2 0 13 13 6340 4134 2514 1450 784
394 194 110 84 62 22 0 0 0 0 0
14 6650 4308 2574 1459 810 458 266 147 70 24 14 3 14 0 0 0 5695 2703 1283 609 289 137 65 31 15 7 3 1 1 1 0 14 6632 4314 2618 1527 856
452 222 107 60 46 34 12 0 0 0 0
15 43416 28162 16936 9748 5474 3024 1632 844 412 198 108 80 54 28 0 0 37280 17694 8398 3986 1892 898 426 202 96 46 22 10 4 2 2 0 43528 28278 17054 9802 5426
2920 1558 846 468 250 122 54 18 4 2 15
16 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 0 0
0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 14 0
32 15 2 4 18 54 122 250 468 846 1558 2920 5426 9802 17054 28278 43528 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398 17694 37280 0 0 28 54 80
108 198 412 844 1632 3024 5474 9748 16936 28162 43416
33 0 0 0 0 12 34 46 60 107 222 452 856 1527 2618 4314 6632 14 0 1 1 1 3 7 15 31 65 137 289 609 1283 2703 5695 0 0 0 14 3
14 24 70 147 266 458 810 1459 2574 4308 6650
34 0 0 0 0 0 22 62 84 110 194 394 784 1450 2514 4134 6340 13 13 0 2 2 2 6 14 30 62 130 274 578 1218 2566 5406 26 0 0 0 26
6 26 44 126 262 470 800 1386 2414 4050 6268
35 12 0 0 0 0 0 30 84 114 150 261 516 996 1782 2961 4548 12 12 12 0 3 3 3 9 21 45 93 195 411 867 1827 3849 36 36 0 0 0
36 9 36 60 168 345 612 1026 1728 2865 4428
36 44 22 0 0 0 0 0 36 100 136 180 308 588 1088 1852 2868 33 11 11 11 0 4 4 4 12 28 60 124 260 548 1156 2436 44 33 44 0 0
0 44 12 44 72 196 396 692 1136 1836 2812
37 100 70 30 0 0 0 0 0 40 110 150 200 335 610 1060 1660 70 30 10 10 10 0 5 5 5 15 35 75 155 325 685 1445 60 50 30 50 0
0 0 50 15 50 80 210 415 710 1130 1710
38 180 126 90 36 0 0 0 0 0 42 114 156 210 342 582 912 135 63 27 9 9 9 0 6 6 6 18 42 90 186 390 822 126 72 54 27 54
0 0 0 54 18 54 84 210 402 666 1008
39 296 200 144 104 40 0 0 0 0 0 42 112 154 210 329 504 248 120 56 24 8 8 8 0 7 7 7 21 49 105 217 455 280 168 80 56 24
56 0 0 0 56 21 56 84 196 357 560
40 504 329 210 154 112 42 0 0 0 0 0 40 104 144 200 296 455 217 105 49 21 7 7 7 0 8 8 8 24 56 120 248 560 357 196 84 56
21 56 0 0 0 56 24 56 80 168 280
41 912 582 342 210 156 114 42 0 0 0 0 0 36 90 126 180 822 390 186 90 42 18 6 6 6 0 9 9 9 27 63 135 1008 666 402 210 84
54 18 54 0 0 0 54 27 54 72 126
42 1660 1060 610 335 200 150 110 40 0 0 0 0 0 30 70 100 1445 685 325 155 75 35 15 5 5 5 0 10 10 10 30 70 1710 1130 710 415 210
80 50 15 50 0 0 0 50 30 50 60
43 2868 1852 1088 588 308 180 136 100 36 0 0 0 0 0 22 44 2436 1156 548 260 124 60 28 12 4 4 4 0 11 11 11 33 2812 1836 1136 692 396
196 72 44 12 44 0 0 0 44 33 44
44 4548 2961 1782 996 516 261 150 114 84 30 0 0 0 0 0 12 3849 1827 867 411 195 93 45 21 9 3 3 3 0 12 12 12 4428 2865 1728 1026 612
345 168 60 36 9 36 0 0 0 36 36
45 6340 4134 2514 1450 784 394 194 110 84 62 22 0 0 0 0 0 5406 2566 1218 578 274 130 62 30 14 6 2 2 2 0 13 13 6268 4050 2414 1386 800
470 262 126 44 26 6 26 0 0 0 26
46 6632 4314 2618 1527 856 452 222 107 60 46 34 12 0 0 0 0 5695 2703 1283 609 289 137 65 31 15 7 3 1 1 1 0 14 6650 4308 2574 1459 810
458 266 147 70 24 14 3 14 0 0 0
47 43528 28278 17054 9802 5426 2920 1558 846 468 250 122 54 18 4 2 15 37280 17694 8398 3986 1892 898 426 202 96 46 22 10 4 2 2 0 43416 28162 16936 9748 5474
3024 1632 844 412 198 108 80 54 28 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*10 + 1*15 + 1*18 + 1*22 + 1*28 + 1*46 + 2*54 + 1*80 + 1*96 + 1*108 + 1*122 + 1*198 + 1*202 + 1*250 + 1*412 + 1*426 + 1*468 + 1*844 + 1*846 + 1*898 + 1*1558 + 1*1632 +
1*1892 + 1*2920 + 1*3024 + 1*3986 + 1*5426 + 1*5474 + 1*8398 + 1*9748 + 1*9802 + 1*16936 + 1*17054 + 1*17694 + 1*28162 + 1*28278 + 1*37280 + 1*43416 + 1*43528) +
4(8*0 + 3*1 + 2*3 + 1*7 + 1*12 + 3*14 + 1*15 + 1*24 + 1*31 + 1*34 + 1*46 + 1*60 + 1*65 + 1*70 + 1*107 + 1*137 + 1*147 + 1*222 + 1*266 + 1*289 + 1*452 + 1*458 + 1*609 + 1*810 + 1*856 + 1*1283 +
1*1459 + 1*1527 + 1*2574 + 1*2618 + 1*2703 + 1*4308 + 1*4314 + 1*5695 + 1*6632 + 1*6650) +
4(9*0 + 3*2 + 2*6 + 2*13 + 1*14 + 1*22 + 3*26 + 1*30 + 1*44 + 2*62 + 1*84 + 1*110 + 1*126 + 1*130 + 1*194 + 1*262 + 1*274 + 1*394 + 1*470 + 1*578 + 1*784 + 1*800 + 1*1218 + 1*1386 + 1*1450 +
1*2414 + 1*2514 + 1*2566 + 1*4050 + 1*4134 + 1*5406 + 1*6268 + 1*6340) +
4(9*0 + 3*3 + 2*9 + 4*12 + 1*21 + 1*30 + 4*36 + 1*45 + 1*60 + 1*84 + 1*93 + 1*114 + 1*150 + 1*168 + 1*195 + 1*261 + 1*345 + 1*411 + 1*516 + 1*612 + 1*867 + 1*996 + 1*1026 + 1*1728 + 1*1782 +
1*1827 + 1*2865 + 1*2961 + 1*3849 + 1*4428 + 1*4548) +
4(9*0 + 3*4 + 3*11 + 2*12 + 1*22 + 1*28 + 2*33 + 1*36 + 5*44 + 1*60 + 1*72 + 1*100 + 1*124 + 1*136 + 1*180 + 1*196 + 1*260 + 1*308 + 1*396 + 1*548 + 1*588 + 1*692 + 1*1088 + 1*1136 + 1*1156 +
1*1836 + 1*1852 + 1*2436 + 1*2812 + 1*2868) +
4(9*0 + 3*5 + 3*10 + 2*15 + 3*30 + 1*35 + 1*40 + 4*50 + 1*60 + 2*70 + 1*75 + 1*80 + 1*100 + 1*110 + 1*150 + 1*155 + 1*200 + 1*210 + 1*325 + 1*335 + 1*415 + 1*610 + 1*685 + 1*710 + 1*1060 +
1*1130 + 1*1445 + 1*1660 + 1*1710) +
4(9*0 + 3*6 + 3*9 + 2*18 + 2*27 + 1*36 + 2*42 + 4*54 + 1*63 + 1*72 + 1*84 + 2*90 + 1*114 + 2*126 + 1*135 + 1*156 + 1*180 + 1*186 + 2*210 + 1*342 + 1*390 + 1*402 + 1*582 + 1*666 + 1*822 + 1*912 +
1*1008) +
4(9*0 + 3*7 + 3*8 + 2*21 + 2*24 + 1*40 + 1*42 + 1*49 + 5*56 + 1*80 + 1*84 + 1*104 + 1*105 + 1*112 + 1*120 + 1*144 + 1*154 + 1*168 + 1*196 + 1*200 + 1*210 + 1*217 + 1*248 + 1*280 + 1*296 +
1*329 + 1*357 + 1*455 + 1*504 + 1*560) +
2(46*0 + 2*14) +
14(48*0)
= 1165676 + 178124 + 169232 + 120804 + 77140 + 47220 + 29748 + 21876 + 56
= 1809876
Value repetition frequencies = 4(41*1 + 2*2 + 1*3) +
4(32*1 + 1*2 + 2*3 + 1*8) +
4(27*1 + 3*2 + 2*3 + 1*9) +
4(26*1 + 1*2 + 1*3 + 2*4 + 1*9) +
4(24*1 + 2*2 + 2*3 + 1*5 + 1*9) +
4(22*1 + 2*2 + 3*3 + 1*4 + 1*9) +
4(17*1 + 6*2 + 2*3 + 1*4 + 1*9) +
4(24*1 + 2*2 + 2*3 + 1*5 + 1*9) +
2(1*2 + 1*46) +
14(1*48)
= 2304
Number of distinct row element sets = 10
Number of rows = 1*2 + 8*4 + 1*14
= 48
Number of distinct values = 203
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 21 22 24
Frequency 1024 12 24 20 20 12 20 16 12 20 16 12 28 8 20 16 12 12 12 12
Distinct values 26 27 28 30 31 33 34 35 36 40 42 44 45 46 49 50 54 56 60 62
Frequency 12 8 8 20 4 8 4 4 24 8 12 24 4 8 4 16 24 20 16 8
Distinct values 63 65 70 72 75 80 84 90 93 96 100 104 105 107 108 110 112 114 120 122
Frequency 4 4 12 8 4 12 16 8 4 4 8 4 4 4 4 8 4 8 4 4
Distinct values 124 126 130 135 136 137 144 147 150 154 155 156 168 180 186 194 195 196 198 200
Frequency 4 12 4 4 4 4 4 4 8 4 4 4 8 8 4 4 4 8 4 8
Distinct values 202 210 217 222 248 250 260 261 262 266 274 280 289 296 308 325 329 335 342 345
Frequency 4 16 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 357 390 394 396 402 411 412 415 426 452 455 458 468 470 504 516 548 560 578 582
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 588 609 610 612 666 685 692 710 784 800 810 822 844 846 856 867 898 912 996 1008
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 1026 1060 1088 1130 1136 1156 1218 1283 1386 1445 1450 1459 1527 1558 1632 1660 1710 1728 1782 1827
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 1836 1852 1892 2414 2436 2514 2566 2574 2618 2703 2812 2865 2868 2920 2961 3024 3849 3986 4050 4134
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 4308 4314 4428 4548 5406 5426 5474 5695 6268 6340 6632 6650 8398 9748 9802 16936 17054 17694 28162 28278
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 37280 43416 43528
Frequency 4 4 4
Sum of distinct value frequencies = 153*4 + 17*8 + 13*12 + 7*16 + 7*20 + 4*24 + 1*28 + 1*1024
= 2304
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 24*39 + 4*40 + 4*45
= 1280
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 976
Number of possible SN-EN pairs with SN != EN = 47*48
= 2256
a = 17, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 140 38
8 172 60
9 432 114
10 668 192
11 1224 342
12 1832 564
13 3168 956
14 5012 1584
15 8548 2686
16 13796 4524
17 22900 7684
18 36952 12968
19 60480 21918
20 97676 36822
21 157532 61378
22 240412 96270
23 360016 148278
24 431232 176978
25 562584 237950
26 472264 195098
27 501632 214196
28 329140 139954
29 250228 109062
30 137476 60890
31 72428 32784
32 30896 14370
33 11328 5370
34 3152 1554
35 752 376
36 48 24
Total 3814220 1585022
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
L
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 0 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 0 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 0 0 0 0 0 0 9 0 0 0
0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0
0 0 0 9 0 0 0 0 0 0 0 0 0 9 0 0 0
7 1 1 1 0 13 0 0 0 0 0 0 0 13 0 1 1 1
2 2 4 8 4 8 4 4 4 4 4 8 4 8 4 2 2
1 1 1 0 13 0 0 0 0 0 0 0 13 0 1 1 1
8 0 0 0 3 0 17 0 0 0 0 0 17 0 3 0 0 0
2 2 2 4 18 4 8 4 4 4 8 4 18 4 2 2 2
0 0 0 3 0 17 0 0 0 0 0 17 0 3 0 0 0
9 3 3 4 4 14 4 25 4 4 4 25 4 14 4 4 3 3
4 4 4 6 8 40 8 12 8 12 8 40 8 6 4 4 4
3 3 4 4 14 4 25 4 4 4 25 4 14 4 4 3 3
10 4 4 4 9 8 36 8 33 8 33 8 36 8 9 4 4 4
4 4 4 4 8 8 66 8 16 8 66 8 8 4 4 4 4
4 4 4 9 8 36 8 33 8 33 8 36 8 9 4 4 4
11 9 10 11 10 22 18 82 18 76 18 82 18 22 10 11 10 9
6 6 6 6 8 18 12 108 12 108 12 18 8 6 6 6 6
9 10 11 10 22 18 82 18 76 18 82 18 22 10 11 10 9
12 12 12 12 17 12 34 24 183 24 183 24 34 12 17 12 12 12
10 10 10 10 10 16 50 20 288 20 50 16 10 10 10 10 10
12 12 12 17 12 34 24 183 24 183 24 34 12 17 12 12 12
13 21 22 24 23 34 28 108 44 488 44 108 28 34 23 24 22 21
20 20 20 20 20 26 36 306 40 306 36 26 20 20 20 20 20
21 22 24 23 34 28 108 44 488 44 108 28 34 23 24 22 21
14 32 33 33 38 34 93 46 501 66 501 46 93 34 38 33 33 32
36 36 36 36 40 36 286 68 492 68 286 36 40 36 36 36 36
32 33 33 38 34 93 46 501 66 501 46 93 34 38 33 33 32
15 57 62 64 64 120 70 659 102 520 102 659 70 120 64 64 62 57
62 62 62 66 62 370 64 552 116 552 64 370 62 66 62 62 62
57 62 64 64 120 70 659 102 520 102 659 70 120 64 64 62 57
16 96 103 104 158 105 918 112 676 152 676 112 918 105 158 104 103 96
102 102 106 102 484 102 1008 108 176 108 1008 102 484 102 106 102 102
96 103 104 158 105 918 112 676 152 676 112 918 105 158 104 103 96
17 167 180 239 186 1304 193 1271 180 444 180 1271 193 1304 186 239 180 167
168 172 168 632 168 1794 164 264 72 264 164 1794 168 632 168 172 168
167 180 239 186 1304 193 1271 180 444 180 1271 193 1304 186 239 180 167
18 280 354 304 1802 306 2408 278 564 98 564 278 2408 306 1802 304 354 280
284 280 834 280 3002 276 718 100 24 100 718 276 3002 280 834 280 284
280 354 304 1802 306 2408 278 564 98 564 278 2408 306 1802 304 354 280
19 534 502 2476 520 4433 488 1083 158 432 158 1083 488 4433 520 2476 502 534
474 1126 474 4784 470 1800 238 52 4 52 238 1800 470 4784 474 1126 474
534 502 2476 520 4433 488 1083 158 432 158 1083 488 4433 520 2476 502 534
20 792 3357 856 7741 821 2294 297 541 96 541 297 2294 821 7741 856 3357 792
1564 806 7328 802 4136 506 188 14 0 14 188 506 4136 802 7328 806 1564
792 3357 856 7741 821 2294 297 541 96 541 297 2294 821 7741 856 3357 792
21 4511 1422 12951 1416 5020 660 1004 143 440 143 1004 660 5020 1416 12951 1422 4511
1368 10874 1364 8790 996 614 64 2 0 2 64 614 996 8790 1364 10874 1368
4511 1422 12951 1416 5020 660 1004 143 440 143 1004 660 5020 1416 12951 1422 4511
22 2256 20812 2396 10696 1353 2039 234 545 98 545 234 2039 1353 10696 2396 20812 2256
15738 2308 17454 1860 1846 224 16 0 0 0 16 224 1846 1860 17454 2308 15738
2256 20812 2396 10696 1353 2039 234 545 98 545 234 2039 1353 10696 2396 20812 2256
23 32149 4010 22000 2684 4360 512 1005 148 440 148 1005 512 4360 2684 22000 4010 32149
3894 32696 3358 5140 658 84 2 0 0 0 2 84 658 5140 3358 32696 3894
32149 4010 22000 2684 4360 512 1005 148 440 148 1005 512 4360 2684 22000 4010 32149
24 6388 43236 5056 9398 1105 2010 241 546 98 546 241 2010 1105 9398 5056 43236 6388
58268 5934 13288 1698 352 18 0 0 0 0 0 18 352 1698 13288 5934 58268
6388 43236 5056 9398 1105 2010 241 546 98 546 241 2010 1105 9398 5056 43236 6388
25 78769 9092 20361 2470 4206 506 1010 147 440 147 1010 506 4206 2470 20361 9092 78769
10344 32026 3972 1286 100 2 0 0 0 0 0 2 100 1286 3972 32026 10344
78769 9092 20361 2470 4206 506 1010 147 440 147 1010 506 4206 2470 20361 9092 78769
26 15244 42023 5332 8771 1013 2017 241 546 98 546 241 2017 1013 8771 5332 42023 15244
72354 8612 4254 420 20 0 0 0 0 0 0 0 20 420 4254 8612 72354
15244 42023 5332 8771 1013 2017 241 546 98 546 241 2017 1013 8771 5332 42023 15244
27 73333 10878 17000 2076 4166 500 1005 146 438 146 1005 500 4166 2076 17000 10878 73333
17606 12976 1462 124 2 0 0 0 0 0 0 0 2 124 1462 12976 17606
73333 10878 17000 2076 4166 500 1005 146 438 146 1005 500 4166 2076 17000 10878 73333
28 19740 26185 4068 7577 985 1964 234 545 98 545 234 1964 985 7577 4068 26185 19740
36832 4426 596 22 0 0 0 0 0 0 0 0 0 22 596 4426 36832
19740 26185 4068 7577 985 1964 234 545 98 545 234 1964 985 7577 4068 26185 19740
29 30899 7234 10142 1864 3328 471 959 140 436 140 959 471 3328 1864 10142 7234 30899
12020 2438 144 2 0 0 0 0 0 0 0 0 0 2 144 2438 12020
30899 7234 10142 1864 3328 471 959 140 436 140 959 471 3328 1864 10142 7234 30899
30 10224 9515 2932 3878 841 1398 217 509 96 509 217 1398 841 3878 2932 9515 10224
8886 704 24 0 0 0 0 0 0 0 0 0 0 0 24 704 8886
10224 9515 2932 3878 841 1398 217 509 96 509 217 1398 841 3878 2932 9515 10224
31 6405 3110 3185 1220 1393 386 594 126 376 126 594 386 1393 1220 3185 3110 6405
2826 172 2 0 0 0 0 0 0 0 0 0 0 0 2 172 2826
6405 3110 3185 1220 1393 386 594 126 376 126 594 386 1393 1220 3185 3110 6405
32 1932 1838 1080 974 466 473 170 269 82 269 170 473 466 974 1080 1838 1932
936 26 0 0 0 0 0 0 0 0 0 0 0 0 0 26 936
1932 1838 1080 974 466 473 170 269 82 269 170 473 466 974 1080 1838 1932
33 581 556 480 327 286 172 173 92 132 92 173 172 286 327 480 556 581
196 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 196
581 556 480 327 286 172 173 92 132 92 173 172 286 327 480 556 581
34 112 145 120 107 81 73 56 56 48 56 56 73 81 107 120 145 112
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28
112 145 120 107 81 73 56 56 48 56 56 73 81 107 120 145 112
35 16 26 25 22 21 22 22 22 22 22 22 22 21 22 25 26 16
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
16 26 25 22 21 22 22 22 22 22 22 22 21 22 25 26 16
36 0 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 0
Total 284568 184728 111266 64065 35852 19806 11160 6986 5752 6986 11160 19806 35852 64065 111266 184728 284568
244036 115830 54980 26106 12416 5946 2932 1622 1256 1622 2932 5946 12416 26106 54980 115830 244036
284568 184728 111266 64065 35852 19806 11160 6986 5752 6986 11160 19806 35852 64065 111266 184728 284568
Grand total = 1256 + 2*1622 + 2*2932 + 2*5946 + 2*12416 + 2*26106 + 2*54980 + 2*115830 + 2*244036 + 2*5752 + 4*6986 + 4*11160 + 4*19806 + 4*35852 + 4*64065 + 4*111266 + 4*184728 + 4*284568
= 3814220
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 8 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 8 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 12 12 12 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 12 12 12 12 12 12 11 7 5 90
11 158 9 14 17 23 24 24 24 24 24 24 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 24 24 24 24 24 24 23 17 14 9 158
12 265 11 17 22 25 33 34 34 34 34 34 33 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 33 34 34 34 34 34 33 25 22 17 11 265
13 445 21 31 36 46 53 63 64 64 64 63 53 46 36 31 21 445
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
445 21 31 36 46 53 63 64 64 64 63 53 46 36 31 21 445
14 741 34 46 55 60 76 89 101 102 101 89 76 60 55 46 34 741
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
741 34 46 55 60 76 89 101 102 101 89 76 60 55 46 34 741
15 1248 63 85 95 107 120 152 173 186 173 152 120 107 95 85 63 1248
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
1248 63 85 95 107 120 152 173 186 173 152 120 107 95 85 63 1248
16 2107 104 139 154 163 181 202 261 276 261 202 181 163 154 139 104 2107
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2107 104 139 154 163 181 202 261 276 261 202 181 163 154 139 104 2107
17 3571 177 241 263 280 295 334 355 416 355 334 295 280 263 241 177 3571
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
3571 177 241 263 280 295 334 355 416 355 334 295 280 263 241 177 3571
18 6039 290 395 433 448 469 472 493 398 493 472 469 448 433 395 290 6039
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6039 290 395 433 448 469 472 493 398 493 472 469 448 433 395 290 6039
19 10200 489 667 731 759 757 726 519 542 519 726 757 759 731 667 489 10200
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
10200 489 667 731 759 757 726 519 542 519 726 757 759 731 667 489 10200
20 17144 822 1113 1220 1234 1171 826 665 448 665 826 1171 1234 1220 1113 822 17144
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17144 822 1113 1220 1234 1171 826 665 448 665 826 1171 1234 1220 1113 822 17144
21 28534 1397 1886 2038 1998 1510 1146 591 564 591 1146 1510 1998 2038 1886 1397 28534
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
28534 1397 1886 2038 1998 1510 1146 591 564 591 1146 1510 1998 2038 1886 1397 28534
22 44507 2361 3156 3317 2721 2103 1010 703 450 703 1010 2103 2721 3317 3156 2361 44507
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
44507 2361 3156 3317 2721 2103 1010 703 450 703 1010 2103 2721 3317 3156 2361 44507
23 68022 3964 5205 4767 3909 1977 1277 601 562 601 1277 1977 3909 4767 5205 3964 68022
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
68022 3964 5205 4767 3909 1977 1277 601 562 601 1277 1977 3909 4767 5205 3964 68022
24 78369 6521 7687 6948 3816 2496 1048 699 448 699 1048 2496 3816 6948 7687 6521 78369
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
78369 6521 7687 6948 3816 2496 1048 699 448 699 1048 2496 3816 6948 7687 6521 78369
25 103404 9638 11333 7108 4936 2084 1272 592 556 592 1272 2084 4936 7108 11333 9638 103404
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
103404 9638 11333 7108 4936 2084 1272 592 556 592 1272 2084 4936 7108 11333 9638 103404
26 74723 14031 11687 9218 4027 2459 1015 687 438 687 1015 2459 4027 9218 11687 14031 74723
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
74723 14031 11687 9218 4027 2459 1015 687 438 687 1015 2459 4027 9218 11687 14031 74723
27 81171 13506 14903 7134 4720 1925 1209 569 540 569 1209 1925 4720 7134 14903 13506 81171
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
81171 13506 14903 7134 4720 1925 1209 569 540 569 1209 1925 4720 7134 14903 13506 81171
28 40547 16525 10009 7956 3311 2171 910 648 416 648 910 2171 3311 7956 10009 16525 40547
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
40547 16525 10009 7956 3311 2171 910 648 416 648 910 2171 3311 7956 10009 16525 40547
29 31674 9274 10331 4558 3480 1459 1031 499 500 499 1031 1459 3480 4558 10331 9274 31674
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
31674 9274 10331 4558 3480 1459 1031 499 500 499 1031 1459 3480 4558 10331 9274 31674
30 12353 8479 4801 4138 1791 1463 636 534 348 534 636 1463 1791 4138 4801 8479 12353
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12353 8479 4801 4138 1791 1463 636 534 348 534 636 1463 1791 4138 4801 8479 12353
31 6097 3488 3429 1750 1506 695 630 322 378 322 630 695 1506 1750 3429 3488 6097
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
6097 3488 3429 1750 1506 695 630 322 378 322 630 695 1506 1750 3429 3488 6097
32 1827 1851 1247 1048 591 515 270 288 174 288 270 515 591 1048 1247 1851 1827
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1827 1851 1247 1048 591 515 270 288 174 288 270 515 591 1048 1247 1851 1827
33 524 570 501 354 300 200 188 120 148 120 188 200 300 354 501 570 524
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
524 570 501 354 300 200 188 120 148 120 188 200 300 354 501 570 524
34 101 147 123 108 85 78 60 60 52 60 60 78 85 108 123 147 101
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
101 147 123 108 85 78 60 60 52 60 60 78 85 108 123 147 101
35 15 26 25 22 22 22 22 22 22 22 22 22 22 22 25 26 15
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
15 26 25 22 22 22 22 22 22 22 22 22 22 22 25 26 15
36 0 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 0
Total 614001 93811 89090 63514 40384 24362 14672 9650 8112 9650 14672 24362 40384 63514 89090 93811 614001
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30
614001 93811 89090 63514 40384 24362 14672 9650 8112 9650 14672 24362 40384 63514 89090 93811 614001
Grand total = 2*30 + 2*8112 + 4*9650 + 4*14672 + 4*24362 + 4*40384 + 4*63514 + 4*89090 + 4*93811 + 4*614001
= 3814220
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
L
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 0 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 0 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 0 0 0 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 0 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 0 0 0 0 0 0 9 5 7 11
12 22 18 12 4 0 0 0 0 0 0 0 4 12 18 22 12
11 7 5 9 0 0 0 0 0 0 0 0 0 9 5 7 11
7 25 24 23 21 23 10 10 10 10 10 10 10 23 21 23 24 25
26 38 40 32 20 12 8 8 8 8 8 12 20 32 40 38 26
25 24 23 21 23 10 10 10 10 10 10 10 23 21 23 24 25
8 32 27 24 31 28 27 10 10 10 10 10 27 28 31 24 27 32
36 62 50 48 46 24 16 12 12 12 16 24 46 48 50 62 36
32 27 24 31 28 27 10 10 10 10 10 27 28 31 24 27 32
9 68 67 72 93 92 76 71 50 50 50 71 76 92 93 72 67 68
76 118 96 104 100 96 56 48 44 48 56 96 100 104 96 118 76
68 67 72 93 92 76 71 50 50 50 71 76 92 93 72 67 68
10 108 100 99 135 156 154 112 103 78 103 112 154 156 135 99 100 108
120 208 176 158 182 180 162 96 92 96 162 180 182 158 176 208 120
108 100 99 135 156 154 112 103 78 103 112 154 156 135 99 100 108
11 201 191 194 252 302 314 308 222 238 222 308 314 302 252 194 191 201
218 358 308 284 304 348 326 284 192 284 326 348 304 284 308 358 218
201 191 194 252 302 314 308 222 238 222 308 314 302 252 194 191 201
12 320 289 280 367 422 475 481 507 368 507 481 475 422 367 280 289 320
346 590 508 466 474 530 598 536 588 536 598 530 474 466 508 590 346
320 289 280 367 422 475 481 507 368 507 481 475 422 367 280 289 320
13 557 518 513 661 770 852 949 951 1200 951 949 852 770 661 513 518 557
600 992 856 802 810 902 1002 1264 1244 1264 1002 902 810 802 856 992 600
557 518 513 661 770 852 949 951 1200 951 949 852 770 661 513 518 557
14 910 842 816 1053 1198 1373 1513 2002 1938 2002 1513 1373 1198 1053 816 842 910
984 1656 1414 1340 1388 1488 1886 2246 2660 2246 1886 1488 1388 1340 1414 1656 984
910 842 816 1053 1198 1373 1513 2002 1938 2002 1513 1373 1198 1053 816 842 910
15 1566 1485 1472 1876 2186 2415 3269 3514 3874 3514 3269 2415 2186 1876 1472 1485 1566
1696 2824 2412 2288 2422 2926 3438 4390 4548 4390 3438 2926 2422 2288 2412 2824 1696
1566 1485 1472 1876 2186 2415 3269 3514 3874 3514 3269 2415 2186 1876 1472 1485 1566
16 2618 2468 2428 3152 3578 4741 5158 6220 6412 6220 5158 4741 3578 3152 2428 2468 2618
2840 4774 4074 3856 4448 5286 6820 7292 7680 7292 6820 5286 4448 3856 4074 4774 2840
2618 2468 2428 3152 3578 4741 5158 6220 6412 6220 5158 4741 3578 3152 2428 2468 2618
17 4472 4238 4259 5451 7328 8009 9877 10367 10690 10367 9877 8009 7328 5451 4259 4238 4472
4846 8114 6950 7016 7906 10650 11840 12526 12220 12526 11840 10650 7906 7016 6950 8114 4846
4472 4238 4259 5451 7328 8009 9877 10367 10690 10367 9877 8009 7328 5451 4259 4238 4472
18 7514 7124 7066 10571 12037 15435 16082 16591 16428 16591 16082 15435 12037 10571 7066 7124 7514
8142 13676 12264 12262 16028 18450 20404 20070 20008 20070 20404 18450 16028 12262 12264 13676 8142
7514 7124 7066 10571 12037 15435 16082 16591 16428 16591 16082 15435 12037 10571 7066 7124 7514
19 12790 12098 14005 17814 24543 25878 26928 26502 26564 26502 26928 25878 24543 17814 14005 12098 12790
13784 23742 21272 25108 28326 32566 32782 32894 32812 32894 32782 32566 28326 25108 21272 23742 13784
12790 12098 14005 17814 24543 25878 26928 26502 26564 26502 26928 25878 24543 17814 14005 12098 12790
20 21412 22775 23279 36955 40512 43517 42847 42223 41512 42223 42847 43517 40512 36955 23279 22775 21412
23880 40520 42270 44534 51396 52378 53076 53336 53636 53336 53076 52378 51396 44534 42270 40520 23880
21412 22775 23279 36955 40512 43517 42847 42223 41512 42223 42847 43517 40512 36955 23279 22775 21412
21 38939 38101 51165 61217 70105 70217 69016 67014 66724 67014 69016 70217 70105 61217 51165 38101 38939
39994 76590 74104 82350 82958 84984 85090 86254 86980 86254 85090 84984 82958 82350 74104 76590 39994
38939 38101 51165 61217 70105 70217 69016 67014 66724 67014 69016 70217 70105 61217 51165 38101 38939
22 58641 78359 81170 105548 109647 108548 104422 102778 101766 102778 104422 108548 109647 105548 81170 78359 58641
74958 125202 131230 126234 128028 128496 131182 132808 132804 132808 131182 128496 128028 126234 131230 125202 74958
58641 78359 81170 105548 109647 108548 104422 102778 101766 102778 104422 108548 109647 105548 81170 78359 58641
23 118793 120991 144949 162946 167127 161031 157377 154879 154874 154879 157377 161031 167127 162946 144949 120991 118793
116168 219034 200882 194774 189126 194432 197872 197870 197932 197870 197872 194432 189126 194774 200882 219034 116168
118793 120991 144949 162946 167127 161031 157377 154879 154874 154879 157377 161031 167127 162946 144949 120991 118793
24 127465 186320 193811 213195 206342 199180 193577 193544 193302 193544 193577 199180 206342 213195 193811 186320 127465
178046 257290 241124 220776 228132 237432 238800 236202 233624 236202 238800 237432 228132 220776 241124 257290 178046
127465 186320 193811 213195 206342 199180 193577 193544 193302 193544 193577 199180 206342 213195 193811 186320 127465
25 239238 254957 270513 279157 273807 261494 257645 256604 257580 256604 257645 261494 273807 279157 270513 254957 239238
240868 373278 307856 288810 297346 309086 311074 306790 305564 306790 311074 309086 297346 288810 307856 373278 240868
239238 254957 270513 279157 273807 261494 257645 256604 257580 256604 257645 261494 273807 279157 270513 254957 239238
26 191511 261148 257532 255460 237223 229491 225499 226054 225362 226054 225499 229491 237223 255460 257532 261148 191511
246518 267328 240152 237200 254826 259908 255544 256388 256740 256388 255544 259908 254826 237200 240152 267328 246518
191511 261148 257532 255460 237223 229491 225499 226054 225362 226054 225499 229491 237223 255460 257532 261148 191511
27 260008 286246 289967 274148 261975 249453 248721 247719 248268 247719 248721 249453 261975 274148 289967 286246 260008
272318 305488 239970 246462 272118 273304 271326 270290 272028 270290 271326 273304 272118 246462 239970 305488 272318
260008 286246 289967 274148 261975 249453 248721 247719 248268 247719 248721 249453 261975 274148 289967 286246 260008
28 185023 223445 204734 191867 174257 170478 167239 167352 166304 167352 167239 170478 174257 191867 204734 223445 185023
210536 154522 148020 165214 174562 177758 176004 177676 177148 177676 176004 177758 174562 165214 148020 154522 210536
185023 223445 204734 191867 174257 170478 167239 167352 166304 167352 167239 170478 174257 191867 204734 223445 185023
29 158815 172493 170564 150335 142225 134180 135024 133167 133386 133167 135024 134180 142225 150335 170564 172493 158815
167598 117064 100020 117726 135262 130748 132810 132948 134276 132948 132810 130748 135262 117726 100020 117064 167598
158815 172493 170564 150335 142225 134180 135024 133167 133386 133167 135024 134180 142225 150335 170564 172493 158815
30 97527 107707 96511 88089 78844 78223 75653 75847 74912 75847 75653 78223 78844 88089 96511 107707 97527
103476 47536 51624 66202 68584 72180 71324 73170 72660 73170 71324 72180 68584 66202 51624 47536 103476
97527 107707 96511 88089 78844 78223 75653 75847 74912 75847 75653 78223 78844 88089 96511 107707 97527
31 56011 58499 55860 47961 45294 42444 42887 41523 41990 41523 42887 42444 45294 47961 55860 58499 56011
57940 20874 23712 31704 36400 35052 37842 37188 37948 37188 37842 35052 36400 31704 23712 20874 57940
56011 58499 55860 47961 45294 42444 42887 41523 41990 41523 42887 42444 45294 47961 55860 58499 56011
32 26135 26911 24528 21954 19845 19651 18745 18930 18398 18930 18745 19651 19845 21954 24528 26911 26135
26738 6018 9044 13100 13714 15154 15068 15992 15424 15992 15068 15154 13714 13100 9044 6018 26738
26135 26911 24528 21954 19845 19651 18745 18930 18398 18930 18745 19651 19845 21954 24528 26911 26135
33 10188 10234 9618 8487 7983 7603 7568 7252 7432 7252 7568 7603 7983 8487 9618 10234 10188
10310 1438 2774 4082 4634 4892 5416 5240 5656 5240 5416 4892 4634 4082 2774 1438 10310
10188 10234 9618 8487 7983 7603 7568 7252 7432 7252 7568 7603 7983 8487 9618 10234 10188
34 3036 2947 2778 2525 2355 2316 2214 2220 2166 2220 2214 2316 2355 2525 2778 2947 3036
3052 160 640 972 1076 1284 1312 1444 1392 1444 1312 1284 1076 972 640 160 3052
3036 2947 2778 2525 2355 2316 2214 2220 2166 2220 2214 2316 2355 2525 2778 2947 3036
35 748 723 701 651 632 618 608 602 600 602 608 618 632 651 701 723 748
750 4 100 144 184 212 232 244 248 244 232 212 184 144 100 4 750
748 723 701 651 632 618 608 602 600 602 608 618 632 651 701 723 748
36 48 48 46 44 44 44 44 44 44 44 44 44 44 44 46 48 48
48 0 4 8 8 8 8 8 8 8 8 8 8 8 4 0 48
48 48 46 44 44 44 44 44 44 44 44 44 44 44 46 48 48
Total 1624745 1881394 1908987 1942025 1890880 1838247 1813854 1804801 1802480 1804801 1813854 1838247 1890880 1942025 1908987 1881394 1624745
1806938 2069548 1863978 1894072 2000812 2050766 2063318 2065514 2066176 2065514 2063318 2050766 2000812 1894072 1863978 2069548 1806938
1624745 1881394 1908987 1942025 1890880 1838247 1813854 1804801 1802480 1804801 1813854 1838247 1890880 1942025 1908987 1881394 1624745
Grand total = 4*1624745 + 2*1802480 + 4*1804801 + 2*1806938 + 4*1813854 + 4*1838247 + 2*1863978 + 2*1863978 + 4*1881394 + 4*1890880 + 2*1894072 + 4*1908987 + 4*1942025 + 2*2000812 + 2*2050766 + 2*2063318 + 2*2065514 + 2066176 +
2*2069548
= 99848716
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48 49 50
EN
0 0 0 30 58 86 116 214 450 932 1822 3418 6286 11442 20512 35738 59430 91592 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398 17694 37280 78546 16 2 4
19 58 132 272 512 932 1734 3296 6236 11526 20680 35876 59484 91592
1 0 0 0 15 3 15 26 77 163 297 516 927 1711 3123 5482 9117 14039 15 0 1 1 1 3 7 15 31 65 137 289 609 1283 2703 5695 11999 0 0 0
0 13 37 50 65 117 247 512 987 1797 3169 5458 9049 13945
2 28 0 0 0 28 6 28 48 140 294 532 916 1620 2918 5148 8616 13300 14 14 0 2 2 2 6 14 30 62 130 274 578 1218 2566 5406 11390 0 0 0
0 0 24 68 92 120 214 444 904 1712 3054 5236 8628 13264
3 39 39 0 0 0 39 9 39 66 189 393 705 1200 2079 3621 6075 9402 13 13 13 0 3 3 3 9 21 45 93 195 411 867 1827 3849 8109 13 0 0
0 0 0 33 93 126 165 291 591 1176 2175 3771 6201 9510
4 48 36 48 0 0 0 48 12 48 80 224 460 816 1368 2304 3820 5904 36 12 12 12 0 4 4 4 12 28 60 124 260 548 1156 2436 5132 48 24 0
0 0 0 0 40 112 152 200 348 688 1328 2376 3948 6064
5 66 55 33 55 0 0 0 55 15 55 90 245 495 865 1420 2295 3515 77 33 11 11 11 0 5 5 5 15 35 75 155 325 685 1445 3045 110 77 33
0 0 0 0 0 45 125 170 225 385 735 1360 2315 3585
6 140 80 60 30 60 0 0 0 60 18 60 96 252 498 852 1356 2052 150 70 30 10 10 10 0 6 6 6 18 42 90 186 390 822 1734 200 140 100
40 0 0 0 0 0 48 132 180 240 402 732 1272 1992
7 315 189 90 63 27 63 0 0 0 63 21 63 98 245 469 777 1176 279 135 63 27 9 9 9 0 7 7 7 21 49 105 217 455 959 333 225 162
117 45 0 0 0 0 0 49 133 182 245 399 679 1064
8 640 408 224 96 64 24 64 0 0 0 64 24 64 96 224 408 640 520 248 120 56 24 8 8 8 0 8 8 8 24 56 120 248 520 576 376 240
176 128 48 0 0 0 0 0 48 128 176 240 376 576
9 1176 777 469 245 98 63 21 63 0 0 0 63 27 63 90 189 315 959 455 217 105 49 21 7 7 7 0 9 9 9 27 63 135 279 1064 679 399
245 182 133 49 0 0 0 0 0 45 117 162 225 333
10 2052 1356 852 498 252 96 60 18 60 0 0 0 60 30 60 80 140 1734 822 390 186 90 42 18 6 6 6 0 10 10 10 30 70 150 1992 1272 732
402 240 180 132 48 0 0 0 0 0 40 100 140 200
11 3515 2295 1420 865 495 245 90 55 15 55 0 0 0 55 33 55 66 3045 1445 685 325 155 75 35 15 5 5 5 0 11 11 11 33 77 3585 2315 1360
735 385 225 170 125 45 0 0 0 0 0 33 77 110
12 5904 3820 2304 1368 816 460 224 80 48 12 48 0 0 0 48 36 48 5132 2436 1156 548 260 124 60 28 12 4 4 4 0 12 12 12 36 6064 3948 2376
1328 688 348 200 152 112 40 0 0 0 0 0 24 48
13 9402 6075 3621 2079 1200 705 393 189 66 39 9 39 0 0 0 39 39 8109 3849 1827 867 411 195 93 45 21 9 3 3 3 0 13 13 13 9510 6201 3771
2175 1176 591 291 165 126 93 33 0 0 0 0 0 13
14 13300 8616 5148 2918 1620 916 532 294 140 48 28 6 28 0 0 0 28 11390 5406 2566 1218 578 274 130 62 30 14 6 2 2 2 0 14 14 13264 8628 5236
3054 1712 904 444 214 120 92 68 24 0 0 0 0 0
15 14039 9117 5482 3123 1711 927 516 297 163 77 26 15 3 15 0 0 0 11999 5695 2703 1283 609 289 137 65 31 15 7 3 1 1 1 0 15 13945 9049 5458
3169 1797 987 512 247 117 65 50 37 13 0 0 0 0
16 91592 59430 35738 20512 11442 6286 3418 1822 932 450 214 116 86 58 30 0 0 78546 37280 17694 8398 3986 1892 898 426 202 96 46 22 10 4 2 2 0 91592 59484 35876
20680 11526 6236 3296 1734 932 512 272 132 58 19 4 2 16
17 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 15 0
34 16 2 4 19 58 132 272 512 932 1734 3296 6236 11526 20680 35876 59484 91592 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398 17694 37280 78546 0 0 30
58 86 116 214 450 932 1822 3418 6286 11442 20512 35738 59430 91592
35 0 0 0 0 13 37 50 65 117 247 512 987 1797 3169 5458 9049 13945 15 0 1 1 1 3 7 15 31 65 137 289 609 1283 2703 5695 11999 0 0 0
15 3 15 26 77 163 297 516 927 1711 3123 5482 9117 14039
36 0 0 0 0 0 24 68 92 120 214 444 904 1712 3054 5236 8628 13264 14 14 0 2 2 2 6 14 30 62 130 274 578 1218 2566 5406 11390 28 0 0
0 28 6 28 48 140 294 532 916 1620 2918 5148 8616 13300
37 13 0 0 0 0 0 33 93 126 165 291 591 1176 2175 3771 6201 9510 13 13 13 0 3 3 3 9 21 45 93 195 411 867 1827 3849 8109 39 39 0
0 0 39 9 39 66 189 393 705 1200 2079 3621 6075 9402
38 48 24 0 0 0 0 0 40 112 152 200 348 688 1328 2376 3948 6064 36 12 12 12 0 4 4 4 12 28 60 124 260 548 1156 2436 5132 48 36 48
0 0 0 48 12 48 80 224 460 816 1368 2304 3820 5904
39 110 77 33 0 0 0 0 0 45 125 170 225 385 735 1360 2315 3585 77 33 11 11 11 0 5 5 5 15 35 75 155 325 685 1445 3045 66 55 33
55 0 0 0 55 15 55 90 245 495 865 1420 2295 3515
40 200 140 100 40 0 0 0 0 0 48 132 180 240 402 732 1272 1992 150 70 30 10 10 10 0 6 6 6 18 42 90 186 390 822 1734 140 80 60
30 60 0 0 0 60 18 60 96 252 498 852 1356 2052
41 333 225 162 117 45 0 0 0 0 0 49 133 182 245 399 679 1064 279 135 63 27 9 9 9 0 7 7 7 21 49 105 217 455 959 315 189 90
63 27 63 0 0 0 63 21 63 98 245 469 777 1176
42 576 376 240 176 128 48 0 0 0 0 0 48 128 176 240 376 576 520 248 120 56 24 8 8 8 0 8 8 8 24 56 120 248 520 640 408 224
96 64 24 64 0 0 0 64 24 64 96 224 408 640
43 1064 679 399 245 182 133 49 0 0 0 0 0 45 117 162 225 333 959 455 217 105 49 21 7 7 7 0 9 9 9 27 63 135 279 1176 777 469
245 98 63 21 63 0 0 0 63 27 63 90 189 315
44 1992 1272 732 402 240 180 132 48 0 0 0 0 0 40 100 140 200 1734 822 390 186 90 42 18 6 6 6 0 10 10 10 30 70 150 2052 1356 852
498 252 96 60 18 60 0 0 0 60 30 60 80 140
45 3585 2315 1360 735 385 225 170 125 45 0 0 0 0 0 33 77 110 3045 1445 685 325 155 75 35 15 5 5 5 0 11 11 11 33 77 3515 2295 1420
865 495 245 90 55 15 55 0 0 0 55 33 55 66
46 6064 3948 2376 1328 688 348 200 152 112 40 0 0 0 0 0 24 48 5132 2436 1156 548 260 124 60 28 12 4 4 4 0 12 12 12 36 5904 3820 2304
1368 816 460 224 80 48 12 48 0 0 0 48 36 48
47 9510 6201 3771 2175 1176 591 291 165 126 93 33 0 0 0 0 0 13 8109 3849 1827 867 411 195 93 45 21 9 3 3 3 0 13 13 13 9402 6075 3621
2079 1200 705 393 189 66 39 9 39 0 0 0 39 39
48 13264 8628 5236 3054 1712 904 444 214 120 92 68 24 0 0 0 0 0 11390 5406 2566 1218 578 274 130 62 30 14 6 2 2 2 0 14 14 13300 8616 5148
2918 1620 916 532 294 140 48 28 6 28 0 0 0 28
49 13945 9049 5458 3169 1797 987 512 247 117 65 50 37 13 0 0 0 0 11999 5695 2703 1283 609 289 137 65 31 15 7 3 1 1 1 0 15 14039 9117 5482
3123 1711 927 516 297 163 77 26 15 3 15 0 0 0
50 91592 59484 35876 20680 11526 6236 3296 1734 932 512 272 132 58 19 4 2 16 78546 37280 17694 8398 3986 1892 898 426 202 96 46 22 10 4 2 2 0 91592 59430 35738
20512 11442 6286 3418 1822 932 450 214 116 86 58 30 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*10 + 1*16 + 1*19 + 1*22 + 1*30 + 1*46 + 2*58 + 1*86 + 1*96 + 1*116 + 1*132 + 1*202 + 1*214 + 1*272 + 1*426 + 1*450 + 1*512 + 1*898 + 2*932 + 1*1734 + 1*1822 + 1*1892 +
1*3296 + 1*3418 + 1*3986 + 1*6236 + 1*6286 + 1*8398 + 1*11442 + 1*11526 + 1*17694 + 1*20512 + 1*20680 + 1*35738 + 1*35876 + 1*37280 + 1*59430 + 1*59484 + 1*78546 + 2*91592) +
4(8*0 + 3*1 + 2*3 + 1*7 + 1*13 + 4*15 + 1*26 + 1*31 + 1*37 + 1*50 + 2*65 + 1*77 + 1*117 + 1*137 + 1*163 + 1*247 + 1*289 + 1*297 + 1*512 + 1*516 + 1*609 + 1*927 + 1*987 + 1*1283 + 1*1711 +
1*1797 + 1*2703 + 1*3123 + 1*3169 + 1*5458 + 1*5482 + 1*5695 + 1*9049 + 1*9117 + 1*11999 + 1*13945 + 1*14039) +
4(9*0 + 3*2 + 2*6 + 3*14 + 1*24 + 3*28 + 1*30 + 1*48 + 1*62 + 1*68 + 1*92 + 1*120 + 1*130 + 1*140 + 1*214 + 1*274 + 1*294 + 1*444 + 1*532 + 1*578 + 1*904 + 1*916 + 1*1218 + 1*1620 + 1*1712 +
1*2566 + 1*2918 + 1*3054 + 1*5148 + 1*5236 + 1*5406 + 1*8616 + 1*8628 + 1*11390 + 1*13264 + 1*13300) +
4(9*0 + 3*3 + 2*9 + 4*13 + 1*21 + 1*33 + 4*39 + 1*45 + 1*66 + 2*93 + 1*126 + 1*165 + 1*189 + 1*195 + 1*291 + 1*393 + 1*411 + 1*591 + 1*705 + 1*867 + 1*1176 + 1*1200 + 1*1827 + 1*2079 + 1*2175 +
1*3621 + 1*3771 + 1*3849 + 1*6075 + 1*6201 + 1*8109 + 1*9402 + 1*9510) +
4(9*0 + 3*4 + 5*12 + 1*24 + 1*28 + 2*36 + 1*40 + 5*48 + 1*60 + 1*80 + 1*112 + 1*124 + 1*152 + 1*200 + 1*224 + 1*260 + 1*348 + 1*460 + 1*548 + 1*688 + 1*816 + 1*1156 + 1*1328 + 1*1368 + 1*2304 +
1*2376 + 1*2436 + 1*3820 + 1*3948 + 1*5132 + 1*5904 + 1*6064) +
4(9*0 + 3*5 + 3*11 + 2*15 + 3*33 + 1*35 + 1*45 + 4*55 + 1*66 + 1*75 + 2*77 + 1*90 + 1*110 + 1*125 + 1*155 + 1*170 + 1*225 + 1*245 + 1*325 + 1*385 + 1*495 + 1*685 + 1*735 + 1*865 + 1*1360 +
1*1420 + 1*1445 + 1*2295 + 1*2315 + 1*3045 + 1*3515 + 1*3585) +
4(9*0 + 3*6 + 3*10 + 2*18 + 2*30 + 1*40 + 1*42 + 1*48 + 4*60 + 1*70 + 1*80 + 1*90 + 1*96 + 1*100 + 1*132 + 2*140 + 1*150 + 1*180 + 1*186 + 1*200 + 1*240 + 1*252 + 1*390 + 1*402 + 1*498 + 1*732 +
1*822 + 1*852 + 1*1272 + 1*1356 + 1*1734 + 1*1992 + 1*2052) +
4(9*0 + 3*7 + 3*9 + 2*21 + 2*27 + 1*45 + 2*49 + 5*63 + 1*90 + 1*98 + 1*105 + 1*117 + 1*133 + 1*135 + 1*162 + 1*182 + 1*189 + 1*217 + 1*225 + 2*245 + 1*279 + 1*315 + 1*333 + 1*399 + 1*455 +
1*469 + 1*679 + 1*777 + 1*959 + 1*1064 + 1*1176) +
2(9*0 + 6*8 + 4*24 + 2*48 + 2*56 + 4*64 + 2*96 + 2*120 + 2*128 + 2*176 + 2*224 + 2*240 + 2*248 + 2*376 + 2*408 + 2*520 + 2*576 + 2*640) +
2(49*0 + 2*15) +
15(51*0)
= 2456004 + 375244 + 356360 + 254056 + 161536 + 97448 + 58688 + 38600 + 16224 + 60
= 3814220
Value repetition frequencies = 4(40*1 + 4*2 + 1*3) +
4(32*1 + 2*2 + 1*3 + 1*4 + 1*8) +
4(31*1 + 1*2 + 3*3 + 1*9) +
4(27*1 + 2*2 + 1*3 + 2*4 + 1*9) +
4(27*1 + 1*2 + 1*3 + 2*5 + 1*9) +
4(25*1 + 2*2 + 3*3 + 1*4 + 1*9) +
4(26*1 + 3*2 + 2*3 + 1*4 + 1*9) +
4(23*1 + 4*2 + 2*3 + 1*5 + 1*9) +
2(14*2 + 2*4 + 1*6 + 1*9) +
2(1*2 + 1*49) +
15(1*51)
= 2601
Number of distinct row element sets = 11
Number of rows = 2*2 + 8*4 + 1*15
= 51
Number of distinct values = 243
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 21
Frequency 1141 12 24 20 20 12 20 16 12 20 16 12 20 20 12 28 4 8 4 12
Distinct values 22 24 26 27 28 30 31 33 35 36 37 39 40 42 45 46 48 49 50 55
Frequency 4 16 4 8 16 16 4 16 4 8 4 16 8 4 12 4 32 8 4 16
Distinct values 56 58 60 62 63 64 65 66 68 70 75 77 80 86 90 92 93 96 98 100
Frequency 4 8 20 4 20 8 8 8 4 4 4 12 8 4 12 4 8 12 4 4
Distinct values 105 110 112 116 117 120 124 125 126 128 130 132 133 135 137 140 150 152 155 162
Frequency 4 4 4 4 8 8 4 4 4 4 4 8 4 4 4 12 4 4 4 4
Distinct values 163 165 170 176 180 182 186 189 195 200 202 214 217 224 225 240 245 247 248 252
Frequency 4 4 4 4 4 4 4 8 4 8 4 8 4 8 8 8 12 4 4 4
Distinct values 260 272 274 279 289 291 294 297 315 325 333 348 376 385 390 393 399 402 408 411
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 426 444 450 455 460 469 495 498 512 516 520 532 548 576 578 591 609 640 679 685
Frequency 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4
Distinct values 688 705 732 735 777 816 822 852 865 867 898 904 916 927 932 959 987 1064 1156 1176
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 8
Distinct values 1200 1218 1272 1283 1328 1356 1360 1368 1420 1445 1620 1711 1712 1734 1797 1822 1827 1892 1992 2052
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4
Distinct values 2079 2175 2295 2304 2315 2376 2436 2566 2703 2918 3045 3054 3123 3169 3296 3418 3515 3585 3621 3771
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 3820 3849 3948 3986 5132 5148 5236 5406 5458 5482 5695 5904 6064 6075 6201 6236 6286 8109 8398 8616
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 8628 9049 9117 9402 9510 11390 11442 11526 11999 13264 13300 13945 14039 17694 20512 20680 35738 35876 37280 59430
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 59484 78546 91592
Frequency 4 4 8
Sum of distinct value frequencies = 186*4 + 25*8 + 12*12 + 8*16 + 8*20 + 1*24 + 1*28 + 1*32 + 1*1141
= 2601
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 26*42 + 4*43 + 4*48
= 1460
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1090
Number of possible SN-EN pairs with SN != EN = 50*51
= 2550
a = 18, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 144 38
8 176 60
9 448 114
10 692 192
11 1272 342
12 1900 564
13 3296 956
14 5216 1584
15 8924 2686
16 14416 4524
17 23980 7684
18 38732 12968
19 63520 21922
20 103004 36952
21 167892 62250
22 270672 104144
23 421760 166918
24 642160 262202
25 819276 335156
26 1102492 464560
27 1004204 413630
28 1129792 481420
29 783392 329932
30 656768 284352
31 381288 166626
32 223644 100028
33 105228 48000
34 43308 20280
35 14836 7074
36 3896 1924
37 864 432
38 52 26
Total 8037344 3339578
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
L
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 0 0 0 0 0 0 0 9 0 0 0
0 0 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0
0 0 0 9 0 0 0 0 0 0 0 0 0 0 9 0 0 0
7 1 1 1 0 13 0 0 0 0 0 0 0 0 13 0 1 1 1
2 2 4 8 4 8 4 4 4 4 4 4 8 4 8 4 2 2
1 1 1 0 13 0 0 0 0 0 0 0 0 13 0 1 1 1
8 0 0 0 3 0 17 0 0 0 0 0 0 17 0 3 0 0 0
2 2 2 4 18 4 8 4 4 4 4 8 4 18 4 2 2 2
0 0 0 3 0 17 0 0 0 0 0 0 17 0 3 0 0 0
9 3 3 4 4 14 4 25 4 4 4 4 25 4 14 4 4 3 3
4 4 4 6 8 40 8 12 8 8 12 8 40 8 6 4 4 4
3 3 4 4 14 4 25 4 4 4 4 25 4 14 4 4 3 3
10 4 4 4 9 8 36 8 33 8 8 33 8 36 8 9 4 4 4
4 4 4 4 8 8 66 8 12 12 8 66 8 8 4 4 4 4
4 4 4 9 8 36 8 33 8 8 33 8 36 8 9 4 4 4
11 9 10 11 10 22 18 82 18 47 47 18 82 18 22 10 11 10 9
6 6 6 6 8 18 12 104 16 16 104 12 18 8 6 6 6 6
9 10 11 10 22 18 82 18 47 47 18 82 18 22 10 11 10 9
12 12 12 12 17 12 34 24 150 57 57 150 24 34 12 17 12 12 12
10 10 10 10 10 16 46 24 154 154 24 46 16 10 10 10 10 10
12 12 12 17 12 34 24 150 57 57 150 24 34 12 17 12 12 12
13 21 22 24 23 34 28 71 81 266 266 81 71 28 34 23 24 22 21
20 20 20 20 20 22 40 122 224 224 122 40 22 20 20 20 20 20
21 22 24 23 34 28 71 81 266 266 81 71 28 34 23 24 22 21
14 32 33 33 38 34 52 87 141 426 426 141 87 52 34 38 33 33 32
36 36 36 36 36 40 44 310 282 282 310 44 40 36 36 36 36 36
32 33 33 38 34 52 87 141 426 426 141 87 52 34 38 33 33 32
15 57 62 64 64 75 115 111 650 323 323 650 111 115 75 64 64 62 57
62 62 62 62 66 62 372 90 582 582 90 372 62 66 62 62 62 62
57 62 64 64 75 115 111 650 323 323 650 111 115 75 64 64 62 57
16 96 103 104 109 154 124 906 203 653 653 203 906 124 154 109 104 103 96
102 102 102 106 102 484 102 1018 186 186 1018 102 484 102 106 102 102 102
96 103 104 109 154 124 906 203 653 653 203 906 124 154 109 104 103 96
17 167 180 186 239 198 1299 236 1247 376 376 1247 236 1299 198 239 186 180 167
168 168 172 168 632 168 1794 166 298 298 166 1794 168 632 168 172 168 168
167 180 186 239 198 1299 236 1247 376 376 1247 236 1299 198 239 186 180 167
18 280 297 361 310 1798 325 2397 366 516 516 366 2397 325 1798 310 361 297 280
280 284 280 834 280 3002 276 718 112 112 718 276 3002 280 834 280 284 280
280 297 361 310 1798 325 2397 366 516 516 366 2397 325 1798 310 361 297 280
19 473 563 516 2480 532 4429 531 1062 345 345 1062 531 4429 532 2480 516 563 473
478 474 1126 474 4784 470 1800 238 54 54 238 1800 470 4784 474 1126 474 478
473 563 516 2480 532 4429 531 1062 345 345 1062 531 4429 532 2480 516 563 473
20 857 839 3374 868 7738 840 2283 386 491 491 386 2283 840 7738 868 3374 839 857
806 1564 806 7328 802 4136 506 188 14 14 188 506 4136 802 7328 806 1564 806
857 839 3374 868 7738 840 2283 386 491 491 386 2283 840 7738 868 3374 839 857
21 1337 4596 1452 12963 1432 5016 704 983 334 334 983 704 5016 1432 12963 1452 4596 1337
2240 1368 10874 1364 8790 996 614 64 2 2 64 614 996 8790 1364 10874 1368 2240
1337 4596 1452 12963 1432 5016 704 983 334 334 983 704 5016 1432 12963 1452 4596 1337
22 6192 2401 20859 2418 10699 1373 2028 323 496 496 323 2028 1373 10699 2418 20859 2401 6192
2312 15738 2308 17454 1860 1846 224 16 0 0 16 224 1846 1860 17454 2308 15738 2312
6192 2401 20859 2418 10699 1373 2028 323 496 496 323 2028 1373 10699 2418 20859 2401 6192
23 3817 32455 4096 22028 2708 4360 556 985 339 339 985 556 4360 2708 22028 4096 32455 3817
22360 3894 32696 3358 5140 658 84 2 0 0 2 84 658 5140 3358 32696 3894 22360
3817 32455 4096 22028 2708 4360 556 985 339 339 985 556 4360 2708 22028 4096 32455 3817
24 48764 6803 43434 5108 9411 1131 2000 330 497 497 330 2000 1131 9411 5108 43434 6803 48764
6566 58268 5934 13288 1698 352 18 0 0 0 0 18 352 1698 13288 5934 58268 6566
48764 6803 43434 5108 9411 1131 2000 330 497 497 330 2000 1131 9411 5108 43434 6803 48764
25 10827 81935 9342 20494 2510 4214 554 990 339 339 990 554 4214 2510 20494 9342 81935 10827
99498 10344 32026 3972 1286 100 2 0 0 0 0 2 100 1286 3972 32026 10344 99498
10827 81935 9342 20494 2510 4214 554 990 339 339 990 554 4214 2510 20494 9342 81935 10827
26 144864 16413 44353 5482 8859 1049 2013 331 497 497 331 2013 1049 8859 5482 44353 16413 144864
17864 72354 8612 4254 420 20 0 0 0 0 0 0 20 420 4254 8612 72354 17864
144864 16413 44353 5482 8859 1049 2013 331 497 497 331 2013 1049 8859 5482 44353 16413 144864
27 27145 92176 11576 18699 2172 4231 556 989 338 338 989 556 4231 2172 18699 11576 92176 27145
154168 17606 12976 1462 124 2 0 0 0 0 0 0 2 124 1462 12976 17606 154168
27145 92176 11576 18699 2172 4231 556 989 338 338 989 556 4231 2172 18699 11576 92176 27145
28 166428 23027 37698 4488 8787 1051 2007 330 497 497 330 2007 1051 8787 4488 37698 23027 166428
34394 36832 4426 596 22 0 0 0 0 0 0 0 0 22 596 4426 36832 34394
166428 23027 37698 4488 8787 1051 2007 330 497 497 330 2007 1051 8787 4488 37698 23027 166428
29 41245 64186 9160 16872 2124 4169 543 984 336 336 984 543 4169 2124 16872 9160 64186 41245
97854 12020 2438 144 2 0 0 0 0 0 0 0 0 2 144 2438 12020 97854
41245 64186 9160 16872 2124 4169 543 984 336 336 984 543 4169 2124 16872 9160 64186 41245
30 86312 17329 25346 4058 7601 1005 1953 323 496 496 323 1953 1005 7601 4058 25346 17329 86312
29924 8886 704 24 0 0 0 0 0 0 0 0 0 0 24 704 8886 29924
86312 17329 25346 4058 7601 1005 1953 323 496 496 323 1953 1005 7601 4058 25346 17329 86312
31 27401 27548 6860 10227 1884 3323 514 937 330 330 937 514 3323 1884 10227 6860 27548 27401
29596 2826 172 2 0 0 0 0 0 0 0 0 0 0 2 172 2826 29596
27401 27548 6860 10227 1884 3323 514 937 330 330 937 514 3323 1884 10227 6860 27548 27401
32 22420 8563 9691 2972 3875 860 1387 306 459 459 306 1387 860 3875 2972 9691 8563 22420
9794 936 26 0 0 0 0 0 0 0 0 0 0 0 0 26 936 9794
22420 8563 9691 2972 3875 860 1387 306 459 459 306 1387 860 3875 2972 9691 8563 22420
33 7183 6576 3218 3194 1231 1388 428 572 287 287 572 428 1388 1231 3194 3218 6576 7183
4262 196 2 0 0 0 0 0 0 0 0 0 0 0 0 2 196 4262
7183 6576 3218 3194 1231 1388 428 572 287 287 572 428 1388 1231 3194 3218 6576 7183
34 2796 2113 1884 1086 970 485 462 237 234 234 237 462 485 970 1086 1884 2113 2796
1092 28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 1092
2796 2113 1884 1086 970 485 462 237 234 234 237 462 485 970 1086 1884 2113 2796
35 673 759 568 479 338 280 197 164 136 136 164 197 280 338 479 568 759 673
228 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 228
673 759 568 479 338 280 197 164 136 136 164 197 280 338 479 568 759 673
36 129 167 146 125 103 87 74 66 62 62 66 74 87 103 125 146 167 129
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30
129 167 146 125 103 87 74 66 62 62 66 74 87 103 125 146 167 129
37 17 28 27 24 23 24 24 24 24 24 24 24 24 23 24 27 28 17
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
17 28 27 24 23 24 24 24 24 24 24 24 24 23 24 27 28 17
38 0 1 1 1 2 2 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 2 2 1 1 1 0
Total 599563 389207 234410 134901 75361 41369 22763 13217 9215 9215 13217 22763 41369 75361 134901 234410 389207 599563
514164 244040 115832 54988 26124 12452 6020 3088 1952 1952 3088 6020 12452 26124 54988 115832 244040 514164
599563 389207 234410 134901 75361 41369 22763 13217 9215 9215 13217 22763 41369 75361 134901 234410 389207 599563
Grand total = 2*1952 + 2*3088 + 2*6020 + 4*9215 + 2*12452 + 4*13217 + 4*22763 + 2*26124 + 4*41369 + 2*54988 + 4*75361 + 2*115832 + 4*134901 + 4*234410 + 2*244040 + 4*389207 + 2*514164 + 4*599563
= 8037344
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 8 8 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 8 8 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 12 12 12 12 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 12 12 12 12 12 12 12 11 7 5 90
11 158 9 14 17 23 24 24 24 24 24 24 24 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 24 24 24 24 24 24 24 23 17 14 9 158
12 265 11 17 22 25 33 34 34 34 34 34 34 33 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 33 34 34 34 34 34 34 33 25 22 17 11 265
13 445 21 31 36 46 53 63 64 64 64 64 63 53 46 36 31 21 445
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
445 21 31 36 46 53 63 64 64 64 64 63 53 46 36 31 21 445
14 741 34 46 55 60 76 89 101 102 102 101 89 76 60 55 46 34 741
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
741 34 46 55 60 76 89 101 102 102 101 89 76 60 55 46 34 741
15 1248 63 85 95 107 120 152 173 187 187 173 152 120 107 95 85 63 1248
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
1248 63 85 95 107 120 152 173 187 187 173 152 120 107 95 85 63 1248
16 2107 104 139 154 163 181 202 262 292 292 262 202 181 163 154 139 104 2107
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2107 104 139 154 163 181 202 262 292 292 262 202 181 163 154 139 104 2107
17 3571 177 241 263 280 295 335 373 459 459 373 335 295 280 263 241 177 3571
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
3571 177 241 263 280 295 335 373 459 459 373 335 295 280 263 241 177 3571
18 6039 290 395 433 448 470 492 550 566 566 550 492 470 448 433 395 290 6039
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6039 290 395 433 448 470 492 550 566 566 550 492 470 448 433 395 290 6039
19 10202 489 667 731 760 779 799 775 677 677 775 799 779 760 731 667 489 10202
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
10202 489 667 731 760 779 799 775 677 677 775 799 779 760 731 667 489 10202
20 17209 822 1113 1221 1258 1262 1198 906 762 762 906 1198 1262 1258 1221 1113 822 17209
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17209 822 1113 1221 1258 1262 1198 906 762 762 906 1198 1262 1258 1221 1113 822 17209
21 28970 1397 1887 2064 2109 2030 1557 1197 761 761 1197 1557 2030 2109 2064 1887 1397 28970
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
28970 1397 1887 2064 2109 2030 1557 1197 761 761 1197 1557 2030 2109 2064 1887 1397 28970
22 48443 2362 3184 3450 3425 2772 2136 1094 802 802 1094 2136 2772 3425 3450 3184 2362 48443
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
48443 2362 3184 3450 3425 2772 2136 1094 802 802 1094 2136 2772 3425 3450 3184 2362 48443
23 77311 3994 5362 5695 4952 3983 2036 1333 773 773 1333 2036 3983 4952 5695 5362 3994 77311
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
77311 3994 5362 5695 4952 3983 2036 1333 773 773 1333 2036 3983 4952 5695 5362 3994 77311
24 120770 6703 8883 8513 7242 3937 2552 1138 802 802 1138 2552 3937 7242 8513 8883 6703 120770
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
120770 6703 8883 8513 7242 3937 2552 1138 802 802 1138 2552 3937 7242 8513 8883 6703 120770
25 150342 11120 13603 12730 7605 5124 2185 1340 769 769 1340 2185 5124 7605 12730 13603 11120 150342
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
150342 11120 13603 12730 7605 5124 2185 1340 769 769 1340 2185 5124 7605 12730 13603 11120 150342
26 205111 17049 20553 14024 10043 4334 2585 1128 796 796 1128 2585 4334 10043 14024 20553 17049 205111
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
205111 17049 20553 14024 10043 4334 2585 1128 796 796 1128 2585 4334 10043 14024 20553 17049 205111
27 165637 25608 23145 18712 8512 5219 2140 1319 758 758 1319 2140 5219 8512 18712 23145 25608 165637
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
165637 25608 23145 18712 8512 5219 2140 1319 758 758 1319 2140 5219 8512 18712 23145 25608 165637
28 190335 27549 30557 15366 10161 4125 2482 1093 780 780 1093 2482 4125 10161 15366 30557 27549 190335
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
190335 27549 30557 15366 10161 4125 2482 1093 780 780 1093 2482 4125 10161 15366 30557 27549 190335
29 103868 35172 22781 17856 7472 4751 1963 1254 730 730 1254 1963 4751 7472 17856 22781 35172 103868
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
103868 35172 22781 17856 7472 4751 1963 1254 730 730 1254 1963 4751 7472 17856 22781 35172 103868
30 90345 22401 25005 11138 8063 3329 2192 984 735 735 984 2192 3329 8063 11138 25005 22401 90345
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90345 22401 25005 11138 8063 3329 2192 984 735 735 984 2192 3329 8063 11138 25005 22401 90345
31 37867 22590 12763 10808 4588 3491 1495 1071 648 648 1071 1495 3491 4588 10808 12763 22590 37867
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
37867 22590 12763 10808 4588 3491 1495 1071 648 648 1071 1495 3491 4588 10808 12763 22590 37867
32 21899 10023 10331 4926 4143 1807 1480 704 598 598 704 1480 1807 4143 4926 10331 10023 21899
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21899 10023 10331 4926 4143 1807 1480 704 598 598 704 1480 1807 4143 4926 10331 10023 21899
33 7254 6452 4059 3454 1758 1515 726 658 430 430 658 726 1515 1758 3454 4059 6452 7254
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
7254 6452 4059 3454 1758 1515 726 658 430 430 658 726 1515 1758 3454 4059 6452 7254
34 2561 2221 1999 1252 1051 603 526 316 298 298 316 526 603 1051 1252 1999 2221 2561
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2561 2221 1999 1252 1051 603 526 316 298 298 316 526 603 1051 1252 1999 2221 2561
35 609 768 597 502 360 304 220 188 160 160 188 220 304 360 502 597 768 609
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
609 768 597 502 360 304 220 188 160 160 188 220 304 360 502 597 768 609
36 117 169 149 126 107 92 78 70 66 66 70 78 92 107 126 149 169 117
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
117 169 149 126 107 92 78 70 66 66 70 78 92 107 126 149 169 117
37 16 28 27 24 24 24 24 24 24 24 24 24 24 24 24 27 28 16
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
16 28 27 24 24 24 24 24 24 24 24 24 24 24 24 27 28 16
38 0 1 1 1 2 2 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 2 2 1 1 1 0
Total 1293655 197639 187652 133691 84811 50759 29791 18199 13123 13123 18199 29791 50759 84811 133691 187652 197639 1293655
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
1293655 197639 187652 133691 84811 50759 29791 18199 13123 13123 18199 29791 50759 84811 133691 187652 197639 1293655
Grand total = 2*32 + 4*13123 + 4*18199 + 4*29791 + 4*50759 + 4*84811 + 4*133691 + 4*187652 + 4*197639 + 4*1293655
= 8037344
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
L
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 0 0 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 0 0 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 0 0 0 0 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 0 0 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 0 0 0 0 0 0 0 9 5 7 11
12 22 18 12 4 0 0 0 0 0 0 0 0 4 12 18 22 12
11 7 5 9 0 0 0 0 0 0 0 0 0 0 9 5 7 11
7 25 24 23 21 23 10 10 10 10 10 10 10 10 23 21 23 24 25
26 38 40 32 20 12 8 8 8 8 8 8 12 20 32 40 38 26
25 24 23 21 23 10 10 10 10 10 10 10 10 23 21 23 24 25
8 32 27 24 31 28 27 10 10 10 10 10 10 27 28 31 24 27 32
36 62 50 48 46 24 16 12 12 12 12 16 24 46 48 50 62 36
32 27 24 31 28 27 10 10 10 10 10 10 27 28 31 24 27 32
9 68 67 72 93 92 76 71 50 50 50 50 71 76 92 93 72 67 68
76 118 96 104 100 96 56 48 44 44 48 56 96 100 104 96 118 76
68 67 72 93 92 76 71 50 50 50 50 71 76 92 93 72 67 68
10 108 100 99 135 156 154 112 103 78 78 103 112 154 156 135 99 100 108
120 208 176 158 182 180 162 96 88 88 96 162 180 182 158 176 208 120
108 100 99 135 156 154 112 103 78 78 103 112 154 156 135 99 100 108
11 201 191 194 252 302 314 308 222 209 209 222 308 314 302 252 194 191 201
218 358 308 284 304 348 326 280 184 184 280 326 348 304 284 308 358 218
201 191 194 252 302 314 308 222 209 209 222 308 314 302 252 194 191 201
12 320 289 280 367 422 475 481 474 351 351 474 481 475 422 367 280 289 320
346 590 508 466 474 530 594 528 446 446 528 594 530 474 466 508 590 346
320 289 280 367 422 475 481 474 351 351 474 481 475 422 367 280 289 320
13 557 518 513 661 770 852 912 930 940 940 930 912 852 770 661 513 518 557
600 992 856 802 810 898 994 1072 1094 1094 1072 994 898 810 802 856 992 600
557 518 513 661 770 852 912 930 940 940 930 912 852 770 661 513 518 557
14 910 842 816 1053 1198 1332 1488 1596 1913 1913 1596 1488 1332 1198 1053 816 842 910
984 1656 1414 1340 1384 1480 1636 2020 2302 2302 2020 1636 1480 1384 1340 1414 1656 984
910 842 816 1053 1198 1332 1488 1596 1913 1913 1596 1488 1332 1198 1053 816 842 910
15 1566 1485 1472 1876 2141 2386 2667 3457 3613 3613 3457 2667 2386 2141 1876 1472 1485 1566
1696 2824 2412 2284 2414 2610 3120 3704 4540 4540 3704 3120 2610 2414 2284 2412 2824 1696
1566 1485 1472 1876 2141 2386 2667 3457 3613 3613 3457 2667 2386 2141 1876 1472 1485 1566
16 2618 2468 2428 3103 3545 3885 5043 5589 6518 6518 5589 5043 3885 3545 3103 2428 2468 2618
2840 4774 4070 3848 4058 4860 5598 7112 7774 7774 7112 5598 4860 4058 3848 4070 4774 2840
2618 2468 2428 3103 3545 3885 5043 5589 6518 6518 5589 5043 3885 3545 3103 2428 2468 2618
17 4472 4238 4206 5414 6152 7802 8530 10463 11091 11091 10463 8530 7802 6152 5414 4206 4238 4472
4846 8110 6942 6544 7356 8600 11292 12372 13032 13032 12372 11292 8600 7356 6544 6942 8110 4846
4472 4238 4206 5414 6152 7802 8530 10463 11091 11091 10463 8530 7802 6152 5414 4206 4238 4472
18 7514 7067 7025 9001 11696 12810 16136 17012 17589 17589 17012 16136 12810 11696 9001 7025 7067 7514
8138 13668 11702 11572 12758 17218 19574 21332 20926 20926 21332 19574 17218 12758 11572 11702 13668 8138
7514 7067 7025 9001 11696 12810 16136 17012 17589 17589 17012 16136 12810 11696 9001 7025 7067 7514
19 12731 12054 11959 17289 19778 25822 27089 28259 28248 28248 28259 27089 25822 19778 17289 11959 12054 12731
13782 23090 20434 20118 25950 30212 34564 34474 34358 34358 34474 34564 30212 25950 20118 20434 23090 13782
12731 12054 11959 17289 19778 25822 27089 28259 28248 28248 28259 27089 25822 19778 17289 11959 12054 12731
20 21489 20254 22570 28846 40264 42756 45447 45072 44647 44647 45072 45447 42756 40264 28846 22570 20254 21489
23196 39656 35062 40506 46082 54700 55690 56354 56104 56104 56354 55690 54700 46082 40506 35062 39656 23196
21489 20254 22570 28846 40264 42756 45447 45072 44647 44647 45072 45447 42756 40264 28846 22570 20254 21489
21 36205 37422 38086 60750 67122 74219 74023 72946 71517 71517 72946 74023 74219 67122 60750 38086 37422 36205
40004 67608 68642 72280 86060 89312 91262 90986 92132 92132 90986 91262 89312 86060 72280 68642 67608 40004
36205 37422 38086 60750 67122 74219 74023 72946 71517 71517 72946 74023 74219 67122 60750 38086 37422 36205
22 64507 62623 82971 100357 118800 120297 118820 115383 113995 113995 115383 118820 120297 118800 100357 82971 62623 64507
67072 125976 120732 137128 141070 146752 146174 147958 149024 149024 147958 146174 146752 141070 137128 120732 125976 67072
64507 62623 82971 100357 118800 120297 118820 115383 113995 113995 115383 118820 120297 118800 100357 82971 62623 64507
23 100400 129088 133583 180706 190005 190090 183423 180228 178276 178276 180228 183423 190090 190005 180706 133583 129088 100400
124652 209804 222166 217964 225212 225384 229592 231760 232108 232108 231760 229592 225384 225212 217964 222166 209804 124652
100400 129088 133583 180706 190005 190090 183423 180228 178276 178276 180228 183423 190090 190005 180706 133583 129088 100400
24 200101 202351 249363 283902 295683 286294 279486 274613 273794 273794 274613 279486 286294 295683 283902 249363 202351 200101
196638 376284 350754 348176 338260 346660 352176 353316 352482 352482 353316 352176 346660 338260 348176 350754 376284 196638
200101 202351 249363 283902 295683 286294 279486 274613 273794 273794 274613 279486 286294 295683 283902 249363 202351 200101
25 231161 335125 348957 395365 388165 375821 364036 362361 362431 362431 362361 364036 375821 388165 395365 348957 335125 231161
320050 480014 460696 423090 432314 447458 453662 451046 445776 445776 451046 453662 447458 432314 423090 460696 480014 320050
231161 335125 348957 395365 388165 375821 364036 362361 362431 362431 362361 364036 375821 388165 395365 348957 335125 231161
26 446357 470752 509732 536273 530214 506816 497678 494602 495977 495977 494602 497678 506816 530214 536273 509732 470752 446357
445474 725166 611864 573450 580608 603470 610186 604490 600886 600886 604490 610186 603470 580608 573450 611864 725166 445474
446357 470752 509732 536273 530214 506816 497678 494602 495977 495977 494602 497678 506816 530214 536273 509732 470752 446357
27 375929 524630 525916 532961 498931 482059 472920 473318 472177 472177 473318 472920 482059 498931 532961 525916 524630 375929
496816 581784 523702 504928 539894 554074 545890 544888 547096 547096 544888 545890 554074 539894 504928 523702 581784 496816
375929 524630 525916 532961 498931 482059 472920 473318 472177 472177 473318 472920 482059 498931 532961 525916 524630 375929
28 558187 611353 624108 602342 578648 551611 548262 546270 546374 546374 546270 548262 551611 578648 602342 624108 611353 558187
579908 711860 562324 560844 609552 618806 614638 610598 614248 614248 610598 614638 618806 609552 560844 562324 711860 579908
558187 611353 624108 602342 578648 551611 548262 546270 546374 546374 546270 548262 551611 578648 602342 624108 611353 558187
29 407186 506369 471871 447419 408688 398372 391431 391387 389394 389394 391387 391431 398372 408688 447419 471871 506369 407186
476500 389464 364994 393658 418524 424918 420214 423362 423316 423316 423362 420214 424918 418524 393658 364994 389464 476500
407186 506369 471871 447419 408688 398372 391431 391387 389394 389394 391387 391431 398372 408688 447419 471871 506369 407186
30 393741 430335 428488 384213 363886 344366 345542 342235 341429 341429 342235 345542 344366 363886 384213 428488 430335 393741
415728 336910 277180 313318 356716 348562 350562 350896 353178 353178 350896 350562 348562 356716 313318 277180 336910 415728
393741 430335 428488 384213 363886 344366 345542 342235 341429 341429 342235 345542 344366 363886 384213 428488 430335 393741
31 254104 287374 258244 237502 213325 210728 204911 204715 203034 203034 204715 204911 210728 213325 237502 258244 287374 254104
274078 146570 151872 186592 194194 201930 200016 203452 203386 203386 203452 200016 201930 194194 186592 151872 146570 274078
254104 287374 258244 237502 213325 210728 204911 204715 203034 203034 204715 204911 210728 213325 237502 258244 287374 254104
32 163135 172512 166395 143298 135412 127017 128037 124960 124930 124930 124960 128037 127017 135412 143298 166395 172512 163135
169990 77428 78280 100762 116148 111384 117630 117208 118082 118082 117208 117630 111384 116148 100762 78280 77428 169990
163135 172512 166395 143298 135412 127017 128037 124960 124930 124930 124960 128037 127017 135412 143298 166395 172512 163135
33 84135 88641 80368 72315 65048 64463 61825 61871 60984 60984 61871 61825 64463 65048 72315 80368 88641 84135
86934 25932 33768 46884 48754 52856 52578 54824 54432 54432 54824 52578 52856 48754 46884 33768 25932 86934
84135 88641 80368 72315 65048 64463 61825 61871 60984 60984 61871 61825 64463 65048 72315 80368 88641 84135
34 37305 37797 35528 30921 29021 27488 27356 26457 26497 26497 26457 27356 27488 29021 30921 35528 37797 37305
38010 7694 11998 17196 19480 19868 21726 21426 22098 22098 21426 21726 19868 19480 17196 11998 7694 38010
37305 37797 35528 30921 29021 27488 27356 26457 26497 26497 26457 27356 27488 29021 30921 35528 37797 37305
35 13524 13568 12648 11377 10537 10291 9916 9796 9676 9676 9796 9916 10291 10537 11377 12648 13568 13524
13664 1646 3466 5190 5682 6452 6696 7048 7120 7120 7048 6696 6452 5682 5190 3466 1646 13664
13524 13568 12648 11377 10537 10291 9916 9796 9676 9676 9796 9916 10291 10537 11377 12648 13568 13524
36 3771 3659 3472 3159 2977 2900 2804 2764 2732 2732 2764 2804 2900 2977 3159 3472 3659 3771
3788 172 744 1124 1280 1500 1596 1708 1740 1740 1708 1596 1500 1280 1124 744 172 3788
3771 3659 3472 3159 2977 2900 2804 2764 2732 2732 2764 2804 2900 2977 3159 3472 3659 3771
37 860 833 809 755 734 718 706 698 694 694 698 706 718 734 755 809 833 860
862 4 108 156 200 232 256 272 280 280 272 256 232 200 156 108 4 862
860 833 809 755 734 718 706 698 694 694 698 706 718 734 755 809 833 860
38 52 52 50 48 48 48 48 48 48 48 48 48 48 48 48 50 52 52
52 0 4 8 8 8 8 8 8 8 8 8 8 8 8 4 0 52
52 52 50 48 48 48 48 48 48 48 48 48 48 48 48 50 52 52
Total 3423297 3964127 4022280 4091814 3983811 3872299 3819528 3797899 3789226 3789226 3797899 3819528 3872299 3983811 4091814 4022280 3964127 3423297
3807150 4360510 3927396 3990870 4215898 4321394 4348492 4354658 4358304 4358304 4354658 4348492 4321394 4215898 3990870 3927396 4360510 3807150
3423297 3964127 4022280 4091814 3983811 3872299 3819528 3797899 3789226 3789226 3797899 3819528 3872299 3983811 4091814 4022280 3964127 3423297
Grand total = 4*3423297 + 4*3789226 + 4*3797899 + 2*3807150 + 4*3819528 + 4*3872299 + 2*3927396 + 4*3964127 + 4*3983811 + 2*3990870 + 4*4022280 + 4*4091814 + 2*4215898 + 2*4321394 + 2*4348492 + 2*4354658 + 2*4358304 + 2*4360510
= 214426468
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
EN
0 0 0 32 62 92 124 230 488 1020 2012 3812 7098 13136 24088 43314 75444 125336 193080 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398
17694 37280 78546 165490 17 2 4 20 62 142 294 556 1018 1910 3672 7046 13250 24306 43474 75440 125206 192874
1 0 0 0 16 3 16 28 84 179 328 574 1044 1963 3672 6656 11584 19195 29536 16 0 1 1 1 3 7 15 31 65 137 289 609 1283
2703 5695 11999 25281 0 0 0 0 14 40 54 70 127 272 572 1118 2067 3720 6602 11466 19079 29424
2 30 0 0 0 30 6 30 52 154 326 594 1032 1854 3422 6246 10964 18234 28078 15 15 0 2 2 2 6 14 30 62 130 274 578 1218
2566 5406 11390 23998 0 0 0 0 0 26 74 100 130 234 494 1024 1974 3594 6338 10916 18098 27890
3 42 42 0 0 0 42 9 42 72 210 441 798 1374 2430 4377 7722 12924 19950 14 14 14 0 3 3 3 9 21 45 93 195 411 867
1827 3849 8109 17085 14 0 0 0 0 0 36 102 138 180 321 666 1356 2568 4581 7854 12942 19896
4 52 39 52 0 0 0 52 12 52 88 252 524 940 1600 2772 4828 8100 12536 39 13 13 13 0 4 4 4 12 28 60 124 260 548
1156 2436 5132 10812 52 26 0 0 0 0 0 44 124 168 220 388 788 1568 2900 5028 8268 12680
5 72 60 36 60 0 0 0 60 15 60 100 280 575 1020 1710 2880 4775 7380 84 36 12 12 12 0 5 5 5 15 35 75 155 325
685 1445 3045 6415 120 84 36 0 0 0 0 0 50 140 190 250 435 860 1660 2970 4935 7580
6 154 88 66 33 66 0 0 0 66 18 66 108 294 594 1038 1704 2754 4218 165 77 33 11 11 11 0 6 6 6 18 42 90 186
390 822 1734 3654 220 154 110 44 0 0 0 0 0 54 150 204 270 462 882 1632 2778 4302
7 350 210 100 70 30 70 0 0 0 70 21 70 112 294 581 994 1582 2394 310 150 70 30 10 10 10 0 7 7 7 21 49 105
217 455 959 2023 370 250 180 130 50 0 0 0 0 0 56 154 210 280 469 854 1484 2324
8 720 459 252 108 72 27 72 0 0 0 72 24 72 112 280 536 888 1344 585 279 135 63 27 9 9 9 0 8 8 8 24 56
120 248 520 1096 648 423 270 198 144 54 0 0 0 0 0 56 152 208 280 456 776 1216
9 1344 888 536 280 112 72 24 72 0 0 0 72 27 72 108 252 459 720 1096 520 248 120 56 24 8 8 8 0 9 9 9 27
63 135 279 585 1216 776 456 280 208 152 56 0 0 0 0 0 54 144 198 270 423 648
10 2394 1582 994 581 294 112 70 21 70 0 0 0 70 30 70 100 210 350 2023 959 455 217 105 49 21 7 7 7 0 10 10 10
30 70 150 310 2324 1484 854 469 280 210 154 56 0 0 0 0 0 50 130 180 250 370
11 4218 2754 1704 1038 594 294 108 66 18 66 0 0 0 66 33 66 88 154 3654 1734 822 390 186 90 42 18 6 6 6 0 11 11
11 33 77 165 4302 2778 1632 882 462 270 204 150 54 0 0 0 0 0 44 110 154 220
12 7380 4775 2880 1710 1020 575 280 100 60 15 60 0 0 0 60 36 60 72 6415 3045 1445 685 325 155 75 35 15 5 5 5 0 12
12 12 36 84 7580 4935 2970 1660 860 435 250 190 140 50 0 0 0 0 0 36 84 120
13 12536 8100 4828 2772 1600 940 524 252 88 52 12 52 0 0 0 52 39 52 10812 5132 2436 1156 548 260 124 60 28 12 4 4 4 0
13 13 13 39 12680 8268 5028 2900 1568 788 388 220 168 124 44 0 0 0 0 0 26 52
14 19950 12924 7722 4377 2430 1374 798 441 210 72 42 9 42 0 0 0 42 42 17085 8109 3849 1827 867 411 195 93 45 21 9 3 3 3
0 14 14 14 19896 12942 7854 4581 2568 1356 666 321 180 138 102 36 0 0 0 0 0 14
15 28078 18234 10964 6246 3422 1854 1032 594 326 154 52 30 6 30 0 0 0 30 23998 11390 5406 2566 1218 578 274 130 62 30 14 6 2 2
2 0 15 15 27890 18098 10916 6338 3594 1974 1024 494 234 130 100 74 26 0 0 0 0 0
16 29536 19195 11584 6656 3672 1963 1044 574 328 179 84 28 16 3 16 0 0 0 25281 11999 5695 2703 1283 609 289 137 65 31 15 7 3 1
1 1 0 16 29424 19079 11466 6602 3720 2067 1118 572 272 127 70 54 40 14 0 0 0 0
17 193080 125336 75444 43314 24088 13136 7098 3812 2012 1020 488 230 124 92 62 32 0 0 165490 78546 37280 17694 8398 3986 1892 898 426 202 96 46 22 10
4 2 2 0 192874 125206 75440 43474 24306 13250 7046 3672 1910 1018 556 294 142 62 20 4 2 17
18 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0
36 17 2 4 20 62 142 294 556 1018 1910 3672 7046 13250 24306 43474 75440 125206 192874 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398
17694 37280 78546 165490 0 0 32 62 92 124 230 488 1020 2012 3812 7098 13136 24088 43314 75444 125336 193080
37 0 0 0 0 14 40 54 70 127 272 572 1118 2067 3720 6602 11466 19079 29424 16 0 1 1 1 3 7 15 31 65 137 289 609 1283
2703 5695 11999 25281 0 0 0 16 3 16 28 84 179 328 574 1044 1963 3672 6656 11584 19195 29536
38 0 0 0 0 0 26 74 100 130 234 494 1024 1974 3594 6338 10916 18098 27890 15 15 0 2 2 2 6 14 30 62 130 274 578 1218
2566 5406 11390 23998 30 0 0 0 30 6 30 52 154 326 594 1032 1854 3422 6246 10964 18234 28078
39 14 0 0 0 0 0 36 102 138 180 321 666 1356 2568 4581 7854 12942 19896 14 14 14 0 3 3 3 9 21 45 93 195 411 867
1827 3849 8109 17085 42 42 0 0 0 42 9 42 72 210 441 798 1374 2430 4377 7722 12924 19950
40 52 26 0 0 0 0 0 44 124 168 220 388 788 1568 2900 5028 8268 12680 39 13 13 13 0 4 4 4 12 28 60 124 260 548
1156 2436 5132 10812 52 39 52 0 0 0 52 12 52 88 252 524 940 1600 2772 4828 8100 12536
41 120 84 36 0 0 0 0 0 50 140 190 250 435 860 1660 2970 4935 7580 84 36 12 12 12 0 5 5 5 15 35 75 155 325
685 1445 3045 6415 72 60 36 60 0 0 0 60 15 60 100 280 575 1020 1710 2880 4775 7380
42 220 154 110 44 0 0 0 0 0 54 150 204 270 462 882 1632 2778 4302 165 77 33 11 11 11 0 6 6 6 18 42 90 186
390 822 1734 3654 154 88 66 33 66 0 0 0 66 18 66 108 294 594 1038 1704 2754 4218
43 370 250 180 130 50 0 0 0 0 0 56 154 210 280 469 854 1484 2324 310 150 70 30 10 10 10 0 7 7 7 21 49 105
217 455 959 2023 350 210 100 70 30 70 0 0 0 70 21 70 112 294 581 994 1582 2394
44 648 423 270 198 144 54 0 0 0 0 0 56 152 208 280 456 776 1216 585 279 135 63 27 9 9 9 0 8 8 8 24 56
120 248 520 1096 720 459 252 108 72 27 72 0 0 0 72 24 72 112 280 536 888 1344
45 1216 776 456 280 208 152 56 0 0 0 0 0 54 144 198 270 423 648 1096 520 248 120 56 24 8 8 8 0 9 9 9 27
63 135 279 585 1344 888 536 280 112 72 24 72 0 0 0 72 27 72 108 252 459 720
46 2324 1484 854 469 280 210 154 56 0 0 0 0 0 50 130 180 250 370 2023 959 455 217 105 49 21 7 7 7 0 10 10 10
30 70 150 310 2394 1582 994 581 294 112 70 21 70 0 0 0 70 30 70 100 210 350
47 4302 2778 1632 882 462 270 204 150 54 0 0 0 0 0 44 110 154 220 3654 1734 822 390 186 90 42 18 6 6 6 0 11 11
11 33 77 165 4218 2754 1704 1038 594 294 108 66 18 66 0 0 0 66 33 66 88 154
48 7580 4935 2970 1660 860 435 250 190 140 50 0 0 0 0 0 36 84 120 6415 3045 1445 685 325 155 75 35 15 5 5 5 0 12
12 12 36 84 7380 4775 2880 1710 1020 575 280 100 60 15 60 0 0 0 60 36 60 72
49 12680 8268 5028 2900 1568 788 388 220 168 124 44 0 0 0 0 0 26 52 10812 5132 2436 1156 548 260 124 60 28 12 4 4 4 0
13 13 13 39 12536 8100 4828 2772 1600 940 524 252 88 52 12 52 0 0 0 52 39 52
50 19896 12942 7854 4581 2568 1356 666 321 180 138 102 36 0 0 0 0 0 14 17085 8109 3849 1827 867 411 195 93 45 21 9 3 3 3
0 14 14 14 19950 12924 7722 4377 2430 1374 798 441 210 72 42 9 42 0 0 0 42 42
51 27890 18098 10916 6338 3594 1974 1024 494 234 130 100 74 26 0 0 0 0 0 23998 11390 5406 2566 1218 578 274 130 62 30 14 6 2 2
2 0 15 15 28078 18234 10964 6246 3422 1854 1032 594 326 154 52 30 6 30 0 0 0 30
52 29424 19079 11466 6602 3720 2067 1118 572 272 127 70 54 40 14 0 0 0 0 25281 11999 5695 2703 1283 609 289 137 65 31 15 7 3 1
1 1 0 16 29536 19195 11584 6656 3672 1963 1044 574 328 179 84 28 16 3 16 0 0 0
53 192874 125206 75440 43474 24306 13250 7046 3672 1910 1018 556 294 142 62 20 4 2 17 165490 78546 37280 17694 8398 3986 1892 898 426 202 96 46 22 10
4 2 2 0 193080 125336 75444 43314 24088 13136 7098 3812 2012 1020 488 230 124 92 62 32 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*10 + 1*17 + 1*20 + 1*22 + 1*32 + 1*46 + 2*62 + 1*92 + 1*96 + 1*124 + 1*142 + 1*202 + 1*230 + 1*294 + 1*426 + 1*488 + 1*556 + 1*898 + 1*1018 + 1*1020 + 1*1892 + 1*1910 +
1*2012 + 1*3672 + 1*3812 + 1*3986 + 1*7046 + 1*7098 + 1*8398 + 1*13136 + 1*13250 + 1*17694 + 1*24088 + 1*24306 + 1*37280 + 1*43314 + 1*43474 + 1*75440 + 1*75444 + 1*78546 + 1*125206 +
1*125336 + 1*165490 + 1*192874 + 1*193080) +
4(8*0 + 3*1 + 2*3 + 1*7 + 1*14 + 1*15 + 3*16 + 1*28 + 1*31 + 1*40 + 1*54 + 1*65 + 1*70 + 1*84 + 1*127 + 1*137 + 1*179 + 1*272 + 1*289 + 1*328 + 1*572 + 1*574 + 1*609 + 1*1044 + 1*1118 + 1*1283 +
1*1963 + 1*2067 + 1*2703 + 1*3672 + 1*3720 + 1*5695 + 1*6602 + 1*6656 + 1*11466 + 1*11584 + 1*11999 + 1*19079 + 1*19195 + 1*25281 + 1*29424 + 1*29536) +
4(9*0 + 3*2 + 2*6 + 1*14 + 2*15 + 1*26 + 4*30 + 1*52 + 1*62 + 1*74 + 1*100 + 2*130 + 1*154 + 1*234 + 1*274 + 1*326 + 1*494 + 1*578 + 1*594 + 1*1024 + 1*1032 + 1*1218 + 1*1854 + 1*1974 + 1*2566 +
1*3422 + 1*3594 + 1*5406 + 1*6246 + 1*6338 + 1*10916 + 1*10964 + 1*11390 + 1*18098 + 1*18234 + 1*23998 + 1*27890 + 1*28078) +
4(9*0 + 3*3 + 2*9 + 4*14 + 1*21 + 1*36 + 4*42 + 1*45 + 1*72 + 1*93 + 1*102 + 1*138 + 1*180 + 1*195 + 1*210 + 1*321 + 1*411 + 1*441 + 1*666 + 1*798 + 1*867 + 1*1356 + 1*1374 + 1*1827 + 1*2430 +
1*2568 + 1*3849 + 1*4377 + 1*4581 + 1*7722 + 1*7854 + 1*8109 + 1*12924 + 1*12942 + 1*17085 + 1*19896 + 1*19950) +
4(9*0 + 3*4 + 2*12 + 3*13 + 1*26 + 1*28 + 2*39 + 1*44 + 5*52 + 1*60 + 1*88 + 2*124 + 1*168 + 1*220 + 1*252 + 1*260 + 1*388 + 1*524 + 1*548 + 1*788 + 1*940 + 1*1156 + 1*1568 + 1*1600 + 1*2436 +
1*2772 + 1*2900 + 1*4828 + 1*5028 + 1*5132 + 1*8100 + 1*8268 + 1*10812 + 1*12536 + 1*12680) +
4(9*0 + 3*5 + 3*12 + 2*15 + 1*35 + 3*36 + 1*50 + 4*60 + 1*72 + 1*75 + 2*84 + 1*100 + 1*120 + 1*140 + 1*155 + 1*190 + 1*250 + 1*280 + 1*325 + 1*435 + 1*575 + 1*685 + 1*860 + 1*1020 + 1*1445 +
1*1660 + 1*1710 + 1*2880 + 1*2970 + 1*3045 + 1*4775 + 1*4935 + 1*6415 + 1*7380 + 1*7580) +
4(9*0 + 3*6 + 3*11 + 2*18 + 2*33 + 1*42 + 1*44 + 1*54 + 4*66 + 1*77 + 1*88 + 1*90 + 1*108 + 1*110 + 1*150 + 2*154 + 1*165 + 1*186 + 1*204 + 1*220 + 1*270 + 1*294 + 1*390 + 1*462 + 1*594 +
1*822 + 1*882 + 1*1038 + 1*1632 + 1*1704 + 1*1734 + 1*2754 + 1*2778 + 1*3654 + 1*4218 + 1*4302) +
4(9*0 + 3*7 + 3*10 + 2*21 + 2*30 + 1*49 + 1*50 + 1*56 + 5*70 + 1*100 + 1*105 + 1*112 + 1*130 + 1*150 + 1*154 + 1*180 + 2*210 + 1*217 + 1*250 + 1*280 + 1*294 + 1*310 + 1*350 + 1*370 + 1*455 +
1*469 + 1*581 + 1*854 + 1*959 + 1*994 + 1*1484 + 1*1582 + 1*2023 + 1*2324 + 1*2394) +
4(9*0 + 3*8 + 3*9 + 2*24 + 2*27 + 1*54 + 2*56 + 1*63 + 4*72 + 1*108 + 1*112 + 1*120 + 1*135 + 1*144 + 1*152 + 1*198 + 1*208 + 1*248 + 1*252 + 1*270 + 1*279 + 2*280 + 1*423 + 1*456 + 1*459 +
1*520 + 1*536 + 1*585 + 1*648 + 1*720 + 1*776 + 1*888 + 1*1096 + 1*1216 + 1*1344) +
2(52*0 + 2*16) +
16(54*0)
= 5174620 + 790556 + 750608 + 534764 + 339244 + 203036 + 119164 + 72796 + 52492 + 64
= 8037344
Value repetition frequencies = 4(47*1 + 2*2 + 1*3) +
4(38*1 + 1*2 + 2*3 + 1*8) +
4(32*1 + 3*2 + 1*3 + 1*4 + 1*9) +
4(32*1 + 1*2 + 1*3 + 2*4 + 1*9) +
4(28*1 + 3*2 + 2*3 + 1*5 + 1*9) +
4(28*1 + 2*2 + 3*3 + 1*4 + 1*9) +
4(29*1 + 3*2 + 2*3 + 1*4 + 1*9) +
4(28*1 + 3*2 + 2*3 + 1*5 + 1*9) +
4(27*1 + 4*2 + 2*3 + 1*4 + 1*9) +
2(1*2 + 1*52) +
16(1*54)
= 2916
Number of distinct row element sets = 11
Number of rows = 1*2 + 9*4 + 1*16
= 54
Number of distinct values = 279
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20
Frequency 1264 12 24 20 20 12 20 16 12 20 16 12 20 12 24 20 16 4 8 4
Distinct values 21 22 24 26 27 28 30 31 32 33 35 36 39 40 42 44 45 46 49 50
Frequency 12 4 8 8 8 8 24 4 4 8 4 16 8 20 4 8 4 4 4 8
Distinct values 52 54 56 60 62 63 65 66 70 72 74 75 77 84 88 90 92 93 96 100
Frequency 24 12 12 20 12 4 4 16 24 24 4 4 4 12 8 4 4 4 4 12
Distinct values 102 105 108 110 112 120 124 127 130 135 137 138 140 142 144 150 152 154 155 165
Frequency 4 4 8 4 8 8 12 4 12 4 4 4 4 4 4 8 4 16 4 4
Distinct values 168 179 180 186 190 195 198 202 204 208 210 217 220 230 234 248 250 252 260 270
Frequency 4 4 8 4 4 4 4 4 4 4 12 4 8 4 4 4 8 8 4 8
Distinct values 272 274 279 280 289 294 310 321 325 326 328 350 370 388 390 411 423 426 435 441
Frequency 4 4 4 16 4 12 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 455 456 459 462 469 488 494 520 524 536 548 556 572 574 575 578 581 585 594 609
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 4
Distinct values 648 666 685 720 776 788 798 822 854 860 867 882 888 898 940 959 994 1018 1020 1024
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 4
Distinct values 1032 1038 1044 1096 1118 1156 1216 1218 1283 1344 1356 1374 1445 1484 1568 1582 1600 1632 1660 1704
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 1710 1734 1827 1854 1892 1910 1963 1974 2012 2023 2067 2324 2394 2430 2436 2566 2568 2703 2754 2772
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 2778 2880 2900 2970 3045 3422 3594 3654 3672 3720 3812 3849 3986 4218 4302 4377 4581 4775 4828 4935
Frequency 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4
Distinct values 5028 5132 5406 5695 6246 6338 6415 6602 6656 7046 7098 7380 7580 7722 7854 8100 8109 8268 8398 10812
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 10916 10964 11390 11466 11584 11999 12536 12680 12924 12942 13136 13250 17085 17694 18098 18234 19079 19195 19896 19950
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 23998 24088 24306 25281 27890 28078 29424 29536 37280 43314 43474 75440 75444 78546 125206 125336 165490 192874 193080
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 220*4 + 22*8 + 15*12 + 7*16 + 8*20 + 6*24 + 1*1264
= 2916
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 28*45 + 4*46 + 4*51
= 1652
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1210
Number of possible SN-EN pairs with SN != EN = 53*54
= 2862
a = 19, b = 3
L C
3 8
4 16
5 32
6 44
7 148
8 180
9 464
10 716
11 1320
12 1968
13 3424
14 5420
15 9300
16 15036
17 25060
18 40512
19 66552
20 108080
21 176784
22 287176
23 465600
24 733484
25 1135280
26 1523228
27 2111372
28 2077648
29 2455040
30 1805832
31 1652696
32 1005740
33 657004
34 331668
35 154316
36 59168
37 19160
38 4752
39 984
40 56
Total 16935268
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
L
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0
0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0
0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0
7 1 1 1 0 13 0 0 0 0 0 0 0 0 0 13 0 1 1 1
2 2 4 8 4 8 4 4 4 4 4 4 4 8 4 8 4 2 2
1 1 1 0 13 0 0 0 0 0 0 0 0 0 13 0 1 1 1
8 0 0 0 3 0 17 0 0 0 0 0 0 0 17 0 3 0 0 0
2 2 2 4 18 4 8 4 4 4 4 4 8 4 18 4 2 2 2
0 0 0 3 0 17 0 0 0 0 0 0 0 17 0 3 0 0 0
9 3 3 4 4 14 4 25 4 4 4 4 4 25 4 14 4 4 3 3
4 4 4 6 8 40 8 12 8 8 8 12 8 40 8 6 4 4 4
3 3 4 4 14 4 25 4 4 4 4 4 25 4 14 4 4 3 3
10 4 4 4 9 8 36 8 33 8 8 8 33 8 36 8 9 4 4 4
4 4 4 4 8 8 66 8 12 8 12 8 66 8 8 4 4 4 4
4 4 4 9 8 36 8 33 8 8 8 33 8 36 8 9 4 4 4
11 9 10 11 10 22 18 82 18 47 18 47 18 82 18 22 10 11 10 9
6 6 6 6 8 18 12 104 12 20 12 104 12 18 8 6 6 6 6
9 10 11 10 22 18 82 18 47 18 47 18 82 18 22 10 11 10 9
12 12 12 12 17 12 34 24 150 24 90 24 150 24 34 12 17 12 12 12
10 10 10 10 10 16 46 20 158 20 158 20 46 16 10 10 10 10 10
12 12 12 17 12 34 24 150 24 90 24 150 24 34 12 17 12 12 12
13 21 22 24 23 34 28 71 44 303 44 303 44 71 28 34 23 24 22 21
20 20 20 20 20 22 36 126 40 408 40 126 36 22 20 20 20 20 20
21 22 24 23 34 28 71 44 303 44 303 44 71 28 34 23 24 22 21
14 32 33 33 38 34 52 46 182 66 786 66 182 46 52 34 38 33 33 32
36 36 36 36 36 36 48 68 524 72 524 68 48 36 36 36 36 36 36
32 33 33 38 34 52 46 182 66 786 66 182 46 52 34 38 33 33 32
15 57 62 64 64 75 70 156 102 871 126 871 102 156 70 75 64 64 62 57
62 62 62 62 62 66 64 398 120 1048 120 398 64 66 62 62 62 62 62
57 62 64 64 75 70 156 102 871 126 871 102 156 70 75 64 64 62 57
16 96 103 104 109 105 173 112 997 180 1154 180 997 112 173 105 109 104 103 96
102 102 102 102 106 102 484 112 1096 196 1096 112 484 102 106 102 102 102 102
96 103 104 109 105 173 112 997 180 1154 180 997 112 173 105 109 104 103 96
17 167 180 186 186 251 193 1342 212 1443 308 1443 212 1342 193 251 186 186 180 167
168 168 168 172 168 632 168 1796 200 524 200 1796 168 632 168 172 168 168 168
167 180 186 186 251 193 1342 212 1443 308 1443 212 1342 193 251 186 186 180 167
18 280 297 304 367 306 1817 314 2485 318 934 318 2485 314 1817 306 367 304 297 280
280 280 284 280 834 280 3002 276 730 200 730 276 3002 280 834 280 284 280 280
280 297 304 367 306 1817 314 2485 318 934 318 2485 314 1817 306 367 304 297 280
19 473 502 577 520 2492 528 4472 510 1249 258 1249 510 4472 528 2492 520 577 502 473
474 478 474 1126 474 4784 470 1800 240 104 240 1800 470 4784 474 1126 474 478 474
473 502 577 520 2492 528 4472 510 1249 258 1249 510 4472 528 2492 520 577 502 473
20 792 904 856 3386 865 7757 829 2372 336 886 336 2372 829 7757 865 3386 856 904 792
810 806 1564 806 7328 802 4136 506 188 28 188 506 4136 802 7328 806 1564 806 810
792 904 856 3386 865 7757 829 2372 336 886 336 2372 829 7757 865 3386 856 904 792
21 1406 1422 4626 1464 12979 1428 5060 683 1174 228 1174 683 5060 1428 12979 1464 4626 1422 1406
1368 2240 1368 10874 1364 8790 996 614 64 4 64 614 996 8790 1364 10874 1368 2240 1368
1406 1422 4626 1464 12979 1428 5060 683 1174 228 1174 683 5060 1428 12979 1464 4626 1422 1406
22 2256 6337 2448 20881 2421 10719 1362 2117 274 894 274 2117 1362 10719 2421 20881 2448 6337 2256
3306 2312 15738 2308 17454 1860 1846 224 16 0 16 224 1846 1860 17454 2308 15738 2312 3306
2256 6337 2448 20881 2421 10719 1362 2117 274 894 274 2117 1362 10719 2421 20881 2448 6337 2256
23 8629 4066 32541 4124 22052 2708 4404 536 1176 238 1176 536 4404 2708 22052 4124 32541 4066 8629
3898 22360 3894 32696 3358 5140 658 84 2 0 2 84 658 5140 3358 32696 3894 22360 3898
8629 4066 32541 4124 22052 2708 4404 536 1176 238 1176 536 4404 2708 22052 4124 32541 4066 8629
24 6448 49240 6948 43486 5121 9437 1121 2089 281 896 281 2089 1121 9437 5121 43486 6948 49240 6448
31380 6566 58268 5934 13288 1698 352 18 0 0 0 18 352 1698 13288 5934 58268 6566 31380
6448 49240 6948 43486 5121 9437 1121 2089 281 896 281 2089 1121 9437 5121 43486 6948 49240 6448
25 72325 11524 82242 9426 20534 2518 4262 534 1182 238 1182 534 4262 2518 20534 9426 82242 11524 72325
11080 99498 10344 32026 3972 1286 100 2 0 0 0 2 100 1286 3972 32026 10344 99498 11080
72325 11524 82242 9426 20534 2518 4262 534 1182 238 1182 534 4262 2518 20534 9426 82242 11524 72325
26 18312 149154 16828 44556 5525 8895 1045 2103 282 896 282 2103 1045 8895 5525 44556 16828 149154 18312
163794 17864 72354 8612 4254 420 20 0 0 0 0 0 20 420 4254 8612 72354 17864 163794
18312 149154 16828 44556 5525 8895 1045 2103 282 896 282 2103 1045 8895 5525 44556 16828 149154 18312
27 255897 29122 95343 11824 18844 2196 4287 540 1181 238 1181 540 4287 2196 18844 11824 95343 29122 255897
30642 154168 17606 12976 1462 124 2 0 0 0 0 0 2 124 1462 12976 17606 154168 30642
255897 29122 95343 11824 18844 2196 4287 540 1181 238 1181 540 4287 2196 18844 11824 95343 29122 255897
28 47636 196143 24196 40033 4629 8898 1057 2103 282 896 282 2103 1057 8898 4629 40033 24196 196143 47636
311704 34394 36832 4426 596 22 0 0 0 0 0 0 0 22 596 4426 36832 34394 311704
47636 196143 24196 40033 4629 8898 1057 2103 282 896 282 2103 1057 8898 4629 40033 24196 196143 47636
29 358459 46842 83030 9856 18583 2204 4282 535 1180 236 1180 535 4282 2204 18583 9856 83030 46842 358459
64884 97854 12020 2438 144 2 0 0 0 0 0 0 0 2 144 2438 12020 97854 64884
358459 46842 83030 9856 18583 2204 4282 535 1180 236 1180 535 4282 2204 18583 9856 83030 46842 358459
30 82488 152293 20616 36864 4469 8834 1041 2096 281 896 281 2096 1041 8834 4469 36864 20616 152293 82488
244518 29924 8886 704 24 0 0 0 0 0 0 0 0 0 24 704 8886 29924 244518
82488 152293 20616 36864 4469 8834 1041 2096 281 896 281 2096 1041 8834 4469 36864 20616 152293 82488
31 226989 40442 60836 8784 16969 2128 4212 522 1174 234 1174 522 4212 2128 16969 8784 60836 40442 226989
69406 29596 2826 172 2 0 0 0 0 0 0 0 0 0 2 172 2826 29596 69406
226989 40442 60836 8784 16969 2128 4212 522 1174 234 1174 522 4212 2128 16969 8784 60836 40442 226989
32 68112 75587 15668 25527 4089 7621 994 2042 274 894 274 2042 994 7621 4089 25527 15668 75587 68112
91392 9794 936 26 0 0 0 0 0 0 0 0 0 0 0 26 936 9794 91392
68112 75587 15668 25527 4089 7621 994 2042 274 894 274 2042 994 7621 4089 25527 15668 75587 68112
33 72561 22428 27720 6966 10248 1879 3366 492 1127 224 1127 492 3366 1879 10248 6966 27720 22428 72561
30244 4262 196 2 0 0 0 0 0 0 0 0 0 0 0 2 196 4262 30244
72561 22428 27720 6966 10248 1879 3366 492 1127 224 1127 492 3366 1879 10248 6966 27720 22428 72561
34 23716 21765 8744 9742 2969 3894 849 1476 256 822 256 1476 849 3894 2969 9742 8744 21765 23716
17070 1092 28 0 0 0 0 0 0 0 0 0 0 0 0 0 28 1092 17070
23716 21765 8744 9742 2969 3894 849 1476 256 822 256 1476 849 3894 2969 9742 8744 21765 23716
35 11801 7102 6755 3228 3205 1226 1430 406 733 198 733 406 1430 1226 3205 3228 6755 7102 11801
4958 228 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 228 4958
11801 7102 6755 3228 3205 1226 1430 406 733 198 733 406 1430 1226 3205 3228 6755 7102 11801
36 3248 3308 2168 1890 1082 989 474 529 202 386 202 529 474 989 1082 1890 2168 3308 3248
1388 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30 1388
3248 3308 2168 1890 1082 989 474 529 202 386 202 529 474 989 1082 1890 2168 3308 3248
37 839 890 772 567 490 332 305 188 208 140 208 188 305 332 490 567 772 890 839
256 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 256
839 890 772 567 490 332 305 188 208 140 208 188 305 332 490 567 772 890 839
38 144 197 168 151 121 109 88 84 72 76 72 84 88 109 121 151 168 197 144
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
144 197 168 151 121 109 88 84 72 76 72 84 88 109 121 151 168 197 144
39 18 30 29 26 25 26 26 26 26 26 26 26 26 26 25 26 29 30 18
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
18 30 29 26 25 26 26 26 26 26 26 26 26 26 25 26 29 30 18
40 0 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 0
Total 1263232 820028 493864 284141 158588 86770 47148 26212 16216 13274 16216 26212 47148 86770 158588 284141 493864 820028 1263232
1083302 514168 244042 115840 55006 26160 12526 6176 3418 2648 3418 6176 12526 26160 55006 115840 244042 514168 1083302
1263232 820028 493864 284141 158588 86770 47148 26212 16216 13274 16216 26212 47148 86770 158588 284141 493864 820028 1263232
Grand total = 2648 + 2*3418 + 2*6176 + 2*12526 + 2*13274 + 4*16216 + 2*26160 + 4*26212 + 4*47148 + 2*55006 + 4*86770 + 2*115840 + 4*158588 + 2*244042 + 4*284141 + 4*493864 + 2*514168 + 4*820028 + 2*1083302 + 4*1263232
= 16935268
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 8 8 8 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 8 8 8 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 12 12 12 12 12 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 12 12 12 12 12 12 12 12 11 7 5 90
11 158 9 14 17 23 24 24 24 24 24 24 24 24 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 24 24 24 24 24 24 24 24 23 17 14 9 158
12 265 11 17 22 25 33 34 34 34 34 34 34 34 33 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 33 34 34 34 34 34 34 34 33 25 22 17 11 265
13 445 21 31 36 46 53 63 64 64 64 64 64 63 53 46 36 31 21 445
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
445 21 31 36 46 53 63 64 64 64 64 64 63 53 46 36 31 21 445
14 741 34 46 55 60 76 89 101 102 102 102 101 89 76 60 55 46 34 741
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
741 34 46 55 60 76 89 101 102 102 102 101 89 76 60 55 46 34 741
15 1248 63 85 95 107 120 152 173 187 188 187 173 152 120 107 95 85 63 1248
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
1248 63 85 95 107 120 152 173 187 188 187 173 152 120 107 95 85 63 1248
16 2107 104 139 154 163 181 202 262 293 308 293 262 202 181 163 154 139 104 2107
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2107 104 139 154 163 181 202 262 293 308 293 262 202 181 163 154 139 104 2107
17 3571 177 241 263 280 295 335 374 477 502 477 374 335 295 280 263 241 177 3571
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
3571 177 241 263 280 295 335 374 477 502 477 374 335 295 280 263 241 177 3571
18 6039 290 395 433 448 470 493 570 623 734 623 570 493 470 448 433 395 290 6039
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6039 290 395 433 448 470 493 570 623 734 623 570 493 470 448 433 395 290 6039
19 10202 489 667 731 760 780 821 848 933 812 933 848 821 780 760 731 667 489 10202
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
10202 489 667 731 760 780 821 848 933 812 933 848 821 780 760 731 667 489 10202
20 17211 822 1113 1221 1259 1286 1289 1278 1003 1076 1003 1278 1289 1286 1259 1221 1113 822 17211
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17211 822 1113 1221 1259 1286 1289 1278 1003 1076 1003 1278 1289 1286 1259 1221 1113 822 17211
21 29039 1397 1887 2065 2135 2141 2077 1608 1367 958 1367 1608 2077 2141 2135 2065 1887 1397 29039
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
29039 1397 1887 2065 2135 2141 2077 1608 1367 958 1367 1608 2077 2141 2135 2065 1887 1397 29039
22 48940 2362 3185 3478 3558 3476 2805 2220 1193 1154 1193 2220 2805 3476 3558 3478 3185 2362 48940
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
48940 2362 3185 3478 3558 3476 2805 2220 1193 1154 1193 2220 2805 3476 3558 3478 3185 2362 48940
23 82123 3995 5392 5852 5880 5026 4042 2092 1505 984 1505 2092 4042 5026 5880 5852 5392 3995 82123
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
82123 3995 5392 5852 5880 5026 4042 2092 1505 984 1505 2092 4042 5026 5880 5852 5392 3995 82123
24 133237 6735 9066 9709 8807 7363 3993 2642 1241 1156 1241 2642 3993 7363 8807 9709 9066 6735 133237
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
133237 6735 9066 9709 8807 7363 3993 2642 1241 1156 1241 2642 3993 7363 8807 9709 9066 6735 133237
25 211867 11330 15115 15001 13227 7793 5225 2253 1517 982 1517 2253 5225 7793 13227 15001 15115 11330 211867
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
211867 11330 15115 15001 13227 7793 5225 2253 1517 982 1517 2253 5225 7793 13227 15001 15115 11330 211867
26 281067 18897 23753 22918 14850 10350 4460 2698 1237 1154 1237 2698 4460 10350 14850 22918 23753 18897 281067
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
281067 18897 23753 22918 14850 10350 4460 2698 1237 1154 1237 2698 4460 10350 14850 22918 23753 18897 281067
27 395399 29796 36729 27110 20116 9012 5434 2250 1508 976 1508 2250 5434 9012 20116 27110 36729 29796 395399
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
395399 29796 36729 27110 20116 9012 5434 2250 1508 976 1508 2250 5434 9012 20116 27110 36729 29796 395399
28 354227 45903 44599 37082 17703 10999 4437 2665 1225 1144 1225 2665 4437 10999 17703 37082 44599 45903 354227
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
354227 45903 44599 37082 17703 10999 4437 2665 1225 1144 1225 2665 4437 10999 17703 37082 44599 45903 354227
29 426466 54138 60781 32420 21672 8853 5277 2187 1485 960 1485 2187 5277 8853 21672 32420 60781 54138 426466
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
426466 54138 60781 32420 21672 8853 5277 2187 1485 960 1485 2187 5277 8853 21672 32420 60781 54138 426466
30 255469 71767 49951 39040 16495 10281 4148 2560 1186 1122 1186 2560 4148 10281 16495 39040 49951 71767 255469
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
255469 71767 49951 39040 16495 10281 4148 2560 1186 1122 1186 2560 4148 10281 16495 39040 49951 71767 255469
31 242757 51866 57763 26270 18340 7505 4789 2008 1415 920 1415 2008 4789 7505 18340 26270 57763 51866 242757
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
242757 51866 57763 26270 18340 7505 4789 2008 1415 920 1415 2008 4789 7505 18340 26270 57763 51866 242757
32 109279 56313 32425 26860 11263 8081 3350 2266 1071 1054 1071 2266 3350 8081 11263 26860 32425 56313 109279
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
109279 56313 32425 26860 11263 8081 3350 2266 1071 1054 1071 2266 3350 8081 11263 26860 32425 56313 109279
33 72524 27230 29043 13334 10840 4599 3527 1535 1220 796 1220 1535 3527 4599 10840 13334 29043 27230 72524
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
72524 27230 29043 13334 10840 4599 3527 1535 1220 796 1220 1535 3527 4599 10840 13334 29043 27230 72524
34 26069 20467 12245 10482 4931 4159 1824 1548 768 848 768 1548 1824 4159 4931 10482 12245 20467 26069
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26069 20467 12245 10482 4931 4159 1824 1548 768 848 768 1548 1824 4159 4931 10482 12245 20467 26069
35 11043 7692 7221 4086 3462 1767 1546 754 766 482 766 754 1546 1767 3462 4086 7221 7692 11043
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
11043 7692 7221 4086 3462 1767 1546 754 766 482 766 754 1546 1767 3462 4086 7221 7692 11043
36 3017 3339 2391 2004 1255 1063 614 572 326 422 326 572 614 1063 1255 2004 2391 3339 3017
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3017 3339 2391 2004 1255 1063 614 572 326 422 326 572 614 1063 1255 2004 2391 3339 3017
37 758 906 797 598 508 364 324 220 228 172 228 220 324 364 508 598 797 906 758
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
758 906 797 598 508 364 324 220 228 172 228 220 324 364 508 598 797 906 758
38 131 199 171 152 125 114 92 88 76 80 76 88 92 114 125 152 171 199 131
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
131 199 171 152 125 114 92 88 76 80 76 88 92 114 125 152 171 199 131
39 17 30 29 26 26 26 26 26 26 26 26 26 26 26 26 26 29 30 17
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
17 30 29 26 26 26 26 26 26 26 26 26 26 26 26 26 29 30 17
40 0 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 0
Total 2725631 416395 395310 281538 178390 106316 61518 35946 23126 19260 23126 35946 61518 106316 178390 281538 395310 416395 2725631
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 34
2725631 416395 395310 281538 178390 106316 61518 35946 23126 19260 23126 35946 61518 106316 178390 281538 395310 416395 2725631
Grand total = 2*34 + 2*19260 + 4*23126 + 4*35946 + 4*61518 + 4*106316 + 4*178390 + 4*281538 + 4*395310 + 4*416395 + 4*2725631
= 16935268
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
L
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 0 0 0 0 0 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 0 0 0 0 0 0 0 0 9 5 7 11
12 22 18 12 4 0 0 0 0 0 0 0 0 0 4 12 18 22 12
11 7 5 9 0 0 0 0 0 0 0 0 0 0 0 9 5 7 11
7 25 24 23 21 23 10 10 10 10 10 10 10 10 10 23 21 23 24 25
26 38 40 32 20 12 8 8 8 8 8 8 8 12 20 32 40 38 26
25 24 23 21 23 10 10 10 10 10 10 10 10 10 23 21 23 24 25
8 32 27 24 31 28 27 10 10 10 10 10 10 10 27 28 31 24 27 32
36 62 50 48 46 24 16 12 12 12 12 12 16 24 46 48 50 62 36
32 27 24 31 28 27 10 10 10 10 10 10 10 27 28 31 24 27 32
9 68 67 72 93 92 76 71 50 50 50 50 50 71 76 92 93 72 67 68
76 118 96 104 100 96 56 48 44 44 44 48 56 96 100 104 96 118 76
68 67 72 93 92 76 71 50 50 50 50 50 71 76 92 93 72 67 68
10 108 100 99 135 156 154 112 103 78 78 78 103 112 154 156 135 99 100 108
120 208 176 158 182 180 162 96 88 84 88 96 162 180 182 158 176 208 120
108 100 99 135 156 154 112 103 78 78 78 103 112 154 156 135 99 100 108
11 201 191 194 252 302 314 308 222 209 180 209 222 308 314 302 252 194 191 201
218 358 308 284 304 348 326 280 180 176 180 280 326 348 304 284 308 358 218
201 191 194 252 302 314 308 222 209 180 209 222 308 314 302 252 194 191 201
12 320 289 280 367 422 475 481 474 318 334 318 474 481 475 422 367 280 289 320
346 590 508 466 474 530 594 524 438 304 438 524 594 530 474 466 508 590 346
320 289 280 367 422 475 481 474 318 334 318 474 481 475 422 367 280 289 320
13 557 518 513 661 770 852 912 893 919 680 919 893 912 852 770 661 513 518 557
600 992 856 802 810 898 990 1064 902 944 902 1064 990 898 810 802 856 992 600
557 518 513 661 770 852 912 893 919 680 919 893 912 852 770 661 513 518 557
14 910 842 816 1053 1198 1332 1447 1571 1507 1888 1507 1571 1447 1332 1198 1053 816 842 910
984 1656 1414 1340 1384 1476 1628 1770 2076 1944 2076 1770 1628 1476 1384 1340 1414 1656 984
910 842 816 1053 1198 1332 1447 1571 1507 1888 1507 1571 1447 1332 1198 1053 816 842 910
15 1566 1485 1472 1876 2141 2341 2638 2855 3556 3352 3556 2855 2638 2341 2141 1876 1472 1485 1566
1696 2824 2412 2284 2410 2602 2804 3386 3854 4532 3854 3386 2804 2602 2410 2284 2412 2824 1696
1566 1485 1472 1876 2141 2341 2638 2855 3556 3352 3556 2855 2638 2341 2141 1876 1472 1485 1566
16 2618 2468 2428 3103 3496 3852 4187 5474 5887 6624 5887 5474 4187 3852 3496 3103 2428 2468 2618
2840 4774 4070 3844 4050 4470 5172 5890 7594 7868 7594 5890 5172 4470 4050 3844 4070 4774 2840
2618 2468 2428 3103 3496 3852 4187 5474 5887 6624 5887 5474 4187 3852 3496 3103 2428 2468 2618
17 4472 4238 4206 5361 6115 6626 8323 9116 11187 11492 11187 9116 8323 6626 6115 5361 4206 4238 4472
4846 8110 6938 6536 6884 8050 9242 11824 12878 13844 12878 11824 9242 8050 6884 6536 6938 8110 4846
4472 4238 4206 5361 6115 6626 8323 9116 11187 11492 11187 9116 8323 6626 6115 5361 4206 4238 4472
18 7514 7067 6968 8960 10126 12469 13511 17066 18010 18750 18010 17066 13511 12469 10126 8960 6968 7067 7514
8138 13664 11694 11010 12068 13948 18342 20502 22188 21844 22188 20502 18342 13948 12068 11010 11694 13664 8138
7514 7067 6968 8960 10126 12469 13511 17066 18010 18750 18010 17066 13511 12469 10126 8960 6968 7067 7514
19 12731 11993 11914 15243 19253 21057 27033 28420 30005 29932 30005 28420 27033 21057 19253 15243 11914 11993 12731
13778 23082 19774 19272 20952 27828 32202 36248 35930 35896 35930 36248 32202 27828 20952 19272 19774 23082 13778
12731 11993 11914 15243 19253 21057 27033 28420 30005 29932 30005 28420 27033 21057 19253 15243 11914 11993 12731
20 21426 20206 19958 28079 32097 42450 44628 47614 47438 47724 47438 47614 44628 42450 32097 28079 19958 20206 21426
23194 38898 34052 33148 41902 49234 57860 58816 58970 58420 58970 58816 57860 49234 41902 33148 34052 38898 23194
21426 20206 19958 28079 32097 42450 44628 47614 47438 47724 47438 47614 44628 42450 32097 28079 19958 20206 21426
21 36286 34243 37073 47465 66364 70874 77607 77495 76967 75820 76967 77495 77607 70874 66364 47465 37073 34243 36286
39210 66564 58286 65588 74906 91474 94762 96410 96164 96600 96164 96410 94762 91474 74906 65588 58286 66564 39210
36286 34243 37073 47465 66364 70874 77607 77495 76967 75820 76967 77495 77607 70874 66364 47465 37073 34243 36286
22 61072 61606 62307 98949 110010 125484 126295 125287 121974 121554 121974 125287 126295 125484 110010 98949 62307 61606 61072
67054 113114 111698 116920 142778 151392 156642 155602 157090 158248 157090 155602 156642 151392 142778 116920 111698 113114 67054
61072 61606 62307 98949 110010 125484 126295 125287 121974 121554 121974 125287 126295 125484 110010 98949 62307 61606 61072
23 107456 103696 134440 164363 201192 205722 205171 199234 196875 195046 196875 199234 205171 205722 201192 164363 134440 103696 107456
112854 207750 196664 226686 238116 252500 251464 253700 255542 255560 255542 253700 251464 252500 238116 226686 196664 207750 112854
107456 103696 134440 164363 201192 205722 205171 199234 196875 195046 196875 199234 205171 205722 201192 164363 134440 103696 107456
24 171005 211127 218016 306066 325083 329645 318995 313452 308803 308680 308803 313452 318995 329645 325083 306066 218016 211127 171005
206790 349656 371386 370792 391654 392518 399042 402418 402772 403432 402772 402418 399042 392518 391654 370792 371386 349656 206790
171005 211127 218016 306066 325083 329645 318995 313452 308803 308680 308803 313452 318995 329645 325083 306066 218016 211127 171005
25 334771 336224 424167 488611 518690 505542 493914 483742 482137 480728 482137 483742 493914 505542 518690 488611 424167 336224 334771
331490 638500 602296 612806 598450 612312 620696 624176 623520 620860 623520 624176 620696 612312 598450 612806 602296 638500 331490
334771 336224 424167 488611 518690 505542 493914 483742 482137 480728 482137 483742 493914 505542 518690 488611 424167 336224 334771
26 413079 590173 614201 717823 714572 694968 671156 665881 664334 666274 664334 665881 671156 694968 714572 717823 614201 590173 413079
563624 871104 854932 791714 804338 826758 841570 841638 832554 830168 832554 841638 841570 826758 804338 791714 854932 871104 563624
413079 590173 614201 717823 714572 694968 671156 665881 664334 666274 664334 665881 671156 694968 714572 717823 614201 590173 413079
27 812657 849336 940972 1007685 1005320 962546 943441 934688 936888 936448 936888 934688 943441 962546 1005320 1007685 940972 849336 812657
805792 1366546 1178588 1110542 1109750 1151094 1167328 1159938 1154816 1151228 1154816 1159938 1167328 1151094 1109750 1110542 1178588 1366546 805792
812657 849336 940972 1007685 1005320 962546 943441 934688 936888 936448 936888 934688 943441 962546 1005320 1007685 940972 849336 812657
28 724609 1027888 1043058 1080816 1020768 985600 964440 964784 961568 961898 961568 964784 964440 985600 1020768 1080816 1043058 1027888 724609
976178 1220054 1107980 1049014 1112376 1147248 1135486 1129780 1131442 1137108 1131442 1129780 1135486 1147248 1112376 1049014 1107980 1220054 976178
724609 1027888 1043058 1080816 1020768 985600 964440 964784 961568 961898 961568 964784 964440 985600 1020768 1080816 1043058 1027888 724609
29 1158456 1260051 1299411 1279576 1236776 1179839 1169582 1164773 1165472 1162994 1165472 1164773 1169582 1179839 1236776 1279576 1299411 1260051 1158456
1193064 1579606 1262112 1231150 1316352 1347346 1342410 1329764 1336028 1338764 1336028 1329764 1342410 1347346 1316352 1231150 1262112 1579606 1193064
1158456 1260051 1299411 1279576 1236776 1179839 1169582 1164773 1165472 1162994 1165472 1164773 1169582 1179839 1236776 1279576 1299411 1260051 1158456
30 867527 1110144 1052840 1012088 929348 903414 887805 888382 883293 883390 883293 888382 887805 903414 929348 1012088 1052840 1110144 867527
1045110 941968 868316 907816 969150 984602 971756 977980 977962 979496 977962 977980 971756 984602 969150 907816 868316 941968 1045110
867527 1110144 1052840 1012088 929348 903414 887805 888382 883293 883390 883293 888382 887805 903414 929348 1012088 1052840 1110144 867527
31 939204 1030148 1032307 942992 895675 849572 850570 844026 842853 839886 842853 844026 850570 849572 895675 942992 1032307 1030148 939204
989678 909548 732214 797422 898014 886388 886536 885574 891636 890396 891636 885574 886536 886388 898014 797422 732214 909548 989678
939204 1030148 1032307 942992 895675 849572 850570 844026 842853 839886 842853 844026 850570 849572 895675 942992 1032307 1030148 939204
32 629389 728883 658942 610221 550221 541526 528280 527963 523170 523872 523170 527963 528280 541526 550221 610221 658942 728883 629389
691764 420966 421272 497810 521150 537214 532064 539546 538612 540760 538612 539546 532064 537214 521150 497810 421272 420966 691764
629389 728883 658942 610221 550221 541526 528280 527963 523170 523872 523170 527963 528280 541526 550221 610221 658942 728883 629389
33 451861 483351 471182 409399 387137 363818 366506 358936 359009 356962 359009 358936 366506 363818 387137 409399 471182 483351 451861
473450 262372 244116 301906 347754 334144 346986 346620 349950 347816 349950 346620 346986 334144 347754 301906 244116 262372 473450
451861 483351 471182 409399 387137 363818 366506 358936 359009 356962 359009 358936 366506 363818 387137 409399 471182 483351 451861
34 251563 270497 243769 220675 197882 196279 188695 189005 185727 186742 185727 189005 188695 196279 197882 220675 243769 270497 251563
262896 96980 114808 153686 159360 170416 168832 175082 173628 175484 173628 175082 168832 170416 159360 153686 114808 96980 262896
251563 270497 243769 220675 197882 196279 188695 189005 185727 186742 185727 189005 188695 196279 197882 220675 243769 270497 251563
35 125987 129615 122810 106127 99900 94020 94311 90885 91558 90168 91558 90885 94311 94020 99900 106127 122810 129615 125987
129296 35978 46740 64476 73560 72716 79238 77780 80472 79360 80472 77780 79238 72716 73560 64476 46740 35978 129296
125987 129615 122810 106127 99900 94020 94311 90885 91558 90168 91558 90885 94311 94020 99900 106127 122810 129615 125987
36 51903 52691 48516 43488 39701 39061 37283 37296 36208 36776 36208 37296 37283 39061 39701 43488 48516 52691 51903
52782 9178 15800 23212 24734 27742 28032 29908 29316 30500 29316 29908 28032 27742 24734 23212 15800 9178 52782
51903 52691 48516 43488 39701 39061 37283 37296 36208 36776 36208 37296 37283 39061 39701 43488 48516 52691 51903
37 17654 17590 16602 14827 13975 13387 13172 12684 12788 12460 12788 12684 13172 13387 13975 14827 16602 17590 17654
17810 1894 4254 6314 7226 7884 8696 8712 9368 8968 9368 8712 8696 7884 7226 6314 4254 1894 17810
17654 17590 16602 14827 13975 13387 13172 12684 12788 12460 12788 12684 13172 13387 13975 14827 16602 17590 17654
38 4618 4487 4262 3909 3683 3608 3462 3440 3350 3384 3350 3440 3462 3608 3683 3909 4262 4487 4618
4636 184 856 1300 1476 1772 1856 2060 2048 2156 2048 2060 1856 1772 1476 1300 856 184 4636
4618 4487 4262 3909 3683 3608 3462 3440 3350 3384 3350 3440 3462 3608 3683 3909 4262 4487 4618
39 980 951 925 867 844 826 812 802 796 794 796 802 812 826 844 867 925 951 980
982 4 116 168 216 252 280 300 312 316 312 300 280 252 216 168 116 4 982
980 951 925 867 844 826 812 802 796 794 796 802 812 826 844 867 925 951 980
40 56 56 54 52 52 52 52 52 52 52 52 52 52 52 52 52 54 56 56
56 0 4 8 8 8 8 8 8 8 8 8 8 8 8 8 4 0 56
56 56 54 52 52 52 52 52 52 52 52 52 52 52 52 52 54 56 56
Total 7212707 8352291 8474831 8621243 8393412 8157818 8045220 7996685 7973006 7965032 7973006 7996685 8045220 8157818 8393412 8621243 8474831 8352291 7212707
8021440 9187390 8274858 8408674 8882958 9105476 9163086 9177464 9188402 9193148 9188402 9177464 9163086 9105476 8882958 8408674 8274858 9187390 8021440
7212707 8352291 8474831 8621243 8393412 8157818 8045220 7996685 7973006 7965032 7973006 7996685 8045220 8157818 8393412 8621243 8474831 8352291 7212707
Grand total = 4*7212707 + 2*7965032 + 4*7973006 + 4*7996685 + 2*8021440 + 4*8045220 + 4*8157818 + 2*8274858 + 4*8352291 + 4*8393412 + 2*8408674 + 4*8474831 + 4*8621243 + 2*8882958 + 2*9105476 + 2*9163086 + 2*9177464 + 2*9187390 +
2*9188402 + 9193148
= 476851560
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
EN
0 0 0 34 66 98 132 246 526 1108 2202 4206 7910 14830 27664 50890 91458 159080 264086 406746 0 2 2 4 10 22 46 96 202 426 898 1892
3986 8398 17694 37280 78546 165490 348674 18 2 4 21 66 152 316 600 1104 2086 4048 7856 14974 27932 51072 91396 158820 263786 406428
1 0 0 0 17 3 17 30 91 195 359 632 1161 2215 4221 7830 14051 24351 40347 62112 17 0 1 1 1 3 7 15 31 65 137 289
609 1283 2703 5695 11999 25281 53265 0 0 0 0 15 43 58 75 137 297 632 1249 2337 4271 7746 13883 24213 40293 62112
2 32 0 0 0 32 6 32 56 168 358 656 1148 2088 3926 7344 13312 23168 38390 59072 16 16 0 2 2 2 6 14 30 62 130 274
578 1218 2566 5406 11390 23998 50562 0 0 0 0 0 28 80 108 140 254 544 1144 2236 4134 7440 13204 22932 38158 58848
3 45 45 0 0 0 45 9 45 78 231 489 891 1548 2781 5133 9369 16446 27351 42117 15 15 15 0 3 3 3 9 21 45 93 195
411 867 1827 3849 8109 17085 35997 15 0 0 0 0 0 39 111 150 195 351 741 1536 2961 5391 9507 16374 27147 41835
4 56 42 56 0 0 0 56 12 56 96 280 588 1064 1832 3240 5836 10296 17232 26600 42 14 14 14 0 4 4 4 12 28 60 124
260 548 1156 2436 5132 10812 22780 56 28 0 0 0 0 0 48 136 184 240 428 888 1808 3424 6108 10472 17256 26528
5 78 65 39 65 0 0 0 65 15 65 110 315 655 1175 2000 3465 6035 10125 15670 91 39 13 13 13 0 5 5 5 15 35 75
155 325 685 1445 3045 6415 13515 130 91 39 0 0 0 0 0 55 155 210 275 485 985 1960 3625 6285 10335 15850
6 168 96 72 36 72 0 0 0 72 18 72 120 336 690 1224 2052 3456 5730 8856 180 84 36 12 12 12 0 6 6 6 18 42
90 186 390 822 1734 3654 7698 240 168 120 48 0 0 0 0 0 60 168 228 300 522 1032 1992 3564 5922 9096
7 385 231 110 77 33 77 0 0 0 77 21 77 126 343 693 1211 1988 3213 4921 341 165 77 33 11 11 11 0 7 7 7 21
49 105 217 455 959 2023 4263 407 275 198 143 55 0 0 0 0 0 63 175 238 315 539 1029 1904 3241 5019
8 800 510 280 120 80 30 80 0 0 0 80 24 80 128 336 664 1136 1808 2736 650 310 150 70 30 10 10 10 0 8 8 8
24 56 120 248 520 1096 2312 720 470 300 220 160 60 0 0 0 0 0 64 176 240 320 536 976 1696 2656
9 1512 999 603 315 126 81 27 81 0 0 0 81 27 81 126 315 603 999 1512 1233 585 279 135 63 27 9 9 9 0 9 9
9 27 63 135 279 585 1233 1368 873 513 315 234 171 63 0 0 0 0 0 63 171 234 315 513 873 1368
10 2736 1808 1136 664 336 128 80 24 80 0 0 0 80 30 80 120 280 510 800 2312 1096 520 248 120 56 24 8 8 8 0 10
10 10 30 70 150 310 650 2656 1696 976 536 320 240 176 64 0 0 0 0 0 60 160 220 300 470 720
11 4921 3213 1988 1211 693 343 126 77 21 77 0 0 0 77 33 77 110 231 385 4263 2023 959 455 217 105 49 21 7 7 7 0
11 11 11 33 77 165 341 5019 3241 1904 1029 539 315 238 175 63 0 0 0 0 0 55 143 198 275 407
12 8856 5730 3456 2052 1224 690 336 120 72 18 72 0 0 0 72 36 72 96 168 7698 3654 1734 822 390 186 90 42 18 6 6 6
0 12 12 12 36 84 180 9096 5922 3564 1992 1032 522 300 228 168 60 0 0 0 0 0 48 120 168 240
13 15670 10125 6035 3465 2000 1175 655 315 110 65 15 65 0 0 0 65 39 65 78 13515 6415 3045 1445 685 325 155 75 35 15 5 5
5 0 13 13 13 39 91 15850 10335 6285 3625 1960 985 485 275 210 155 55 0 0 0 0 0 39 91 130
14 26600 17232 10296 5836 3240 1832 1064 588 280 96 56 12 56 0 0 0 56 42 56 22780 10812 5132 2436 1156 548 260 124 60 28 12 4
4 4 0 14 14 14 42 26528 17256 10472 6108 3424 1808 888 428 240 184 136 48 0 0 0 0 0 28 56
15 42117 27351 16446 9369 5133 2781 1548 891 489 231 78 45 9 45 0 0 0 45 45 35997 17085 8109 3849 1827 867 411 195 93 45 21 9
3 3 3 0 15 15 15 41835 27147 16374 9507 5391 2961 1536 741 351 195 150 111 39 0 0 0 0 0 15
16 59072 38390 23168 13312 7344 3926 2088 1148 656 358 168 56 32 6 32 0 0 0 32 50562 23998 11390 5406 2566 1218 578 274 130 62 30 14
6 2 2 2 0 16 16 58848 38158 22932 13204 7440 4134 2236 1144 544 254 140 108 80 28 0 0 0 0 0
17 62112 40347 24351 14051 7830 4221 2215 1161 632 359 195 91 30 17 3 17 0 0 0 53265 25281 11999 5695 2703 1283 609 289 137 65 31 15
7 3 1 1 1 0 17 62112 40293 24213 13883 7746 4271 2337 1249 632 297 137 75 58 43 15 0 0 0 0
18 406746 264086 159080 91458 50890 27664 14830 7910 4206 2202 1108 526 246 132 98 66 34 0 0 348674 165490 78546 37280 17694 8398 3986 1892 898 426 202 96
46 22 10 4 2 2 0 406428 263786 158820 91396 51072 27932 14974 7856 4048 2086 1104 600 316 152 66 21 4 2 18
19 0 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 0
38 18 2 4 21 66 152 316 600 1104 2086 4048 7856 14974 27932 51072 91396 158820 263786 406428 0 2 2 4 10 22 46 96 202 426 898 1892
3986 8398 17694 37280 78546 165490 348674 0 0 34 66 98 132 246 526 1108 2202 4206 7910 14830 27664 50890 91458 159080 264086 406746
39 0 0 0 0 15 43 58 75 137 297 632 1249 2337 4271 7746 13883 24213 40293 62112 17 0 1 1 1 3 7 15 31 65 137 289
609 1283 2703 5695 11999 25281 53265 0 0 0 17 3 17 30 91 195 359 632 1161 2215 4221 7830 14051 24351 40347 62112
40 0 0 0 0 0 28 80 108 140 254 544 1144 2236 4134 7440 13204 22932 38158 58848 16 16 0 2 2 2 6 14 30 62 130 274
578 1218 2566 5406 11390 23998 50562 32 0 0 0 32 6 32 56 168 358 656 1148 2088 3926 7344 13312 23168 38390 59072
41 15 0 0 0 0 0 39 111 150 195 351 741 1536 2961 5391 9507 16374 27147 41835 15 15 15 0 3 3 3 9 21 45 93 195
411 867 1827 3849 8109 17085 35997 45 45 0 0 0 45 9 45 78 231 489 891 1548 2781 5133 9369 16446 27351 42117
42 56 28 0 0 0 0 0 48 136 184 240 428 888 1808 3424 6108 10472 17256 26528 42 14 14 14 0 4 4 4 12 28 60 124
260 548 1156 2436 5132 10812 22780 56 42 56 0 0 0 56 12 56 96 280 588 1064 1832 3240 5836 10296 17232 26600
43 130 91 39 0 0 0 0 0 55 155 210 275 485 985 1960 3625 6285 10335 15850 91 39 13 13 13 0 5 5 5 15 35 75
155 325 685 1445 3045 6415 13515 78 65 39 65 0 0 0 65 15 65 110 315 655 1175 2000 3465 6035 10125 15670
44 240 168 120 48 0 0 0 0 0 60 168 228 300 522 1032 1992 3564 5922 9096 180 84 36 12 12 12 0 6 6 6 18 42
90 186 390 822 1734 3654 7698 168 96 72 36 72 0 0 0 72 18 72 120 336 690 1224 2052 3456 5730 8856
45 407 275 198 143 55 0 0 0 0 0 63 175 238 315 539 1029 1904 3241 5019 341 165 77 33 11 11 11 0 7 7 7 21
49 105 217 455 959 2023 4263 385 231 110 77 33 77 0 0 0 77 21 77 126 343 693 1211 1988 3213 4921
46 720 470 300 220 160 60 0 0 0 0 0 64 176 240 320 536 976 1696 2656 650 310 150 70 30 10 10 10 0 8 8 8
24 56 120 248 520 1096 2312 800 510 280 120 80 30 80 0 0 0 80 24 80 128 336 664 1136 1808 2736
47 1368 873 513 315 234 171 63 0 0 0 0 0 63 171 234 315 513 873 1368 1233 585 279 135 63 27 9 9 9 0 9 9
9 27 63 135 279 585 1233 1512 999 603 315 126 81 27 81 0 0 0 81 27 81 126 315 603 999 1512
48 2656 1696 976 536 320 240 176 64 0 0 0 0 0 60 160 220 300 470 720 2312 1096 520 248 120 56 24 8 8 8 0 10
10 10 30 70 150 310 650 2736 1808 1136 664 336 128 80 24 80 0 0 0 80 30 80 120 280 510 800
49 5019 3241 1904 1029 539 315 238 175 63 0 0 0 0 0 55 143 198 275 407 4263 2023 959 455 217 105 49 21 7 7 7 0
11 11 11 33 77 165 341 4921 3213 1988 1211 693 343 126 77 21 77 0 0 0 77 33 77 110 231 385
50 9096 5922 3564 1992 1032 522 300 228 168 60 0 0 0 0 0 48 120 168 240 7698 3654 1734 822 390 186 90 42 18 6 6 6
0 12 12 12 36 84 180 8856 5730 3456 2052 1224 690 336 120 72 18 72 0 0 0 72 36 72 96 168
51 15850 10335 6285 3625 1960 985 485 275 210 155 55 0 0 0 0 0 39 91 130 13515 6415 3045 1445 685 325 155 75 35 15 5 5
5 0 13 13 13 39 91 15670 10125 6035 3465 2000 1175 655 315 110 65 15 65 0 0 0 65 39 65 78
52 26528 17256 10472 6108 3424 1808 888 428 240 184 136 48 0 0 0 0 0 28 56 22780 10812 5132 2436 1156 548 260 124 60 28 12 4
4 4 0 14 14 14 42 26600 17232 10296 5836 3240 1832 1064 588 280 96 56 12 56 0 0 0 56 42 56
53 41835 27147 16374 9507 5391 2961 1536 741 351 195 150 111 39 0 0 0 0 0 15 35997 17085 8109 3849 1827 867 411 195 93 45 21 9
3 3 3 0 15 15 15 42117 27351 16446 9369 5133 2781 1548 891 489 231 78 45 9 45 0 0 0 45 45
54 58848 38158 22932 13204 7440 4134 2236 1144 544 254 140 108 80 28 0 0 0 0 0 50562 23998 11390 5406 2566 1218 578 274 130 62 30 14
6 2 2 2 0 16 16 59072 38390 23168 13312 7344 3926 2088 1148 656 358 168 56 32 6 32 0 0 0 32
55 62112 40293 24213 13883 7746 4271 2337 1249 632 297 137 75 58 43 15 0 0 0 0 53265 25281 11999 5695 2703 1283 609 289 137 65 31 15
7 3 1 1 1 0 17 62112 40347 24351 14051 7830 4221 2215 1161 632 359 195 91 30 17 3 17 0 0 0
56 406428 263786 158820 91396 51072 27932 14974 7856 4048 2086 1104 600 316 152 66 21 4 2 18 348674 165490 78546 37280 17694 8398 3986 1892 898 426 202 96
46 22 10 4 2 2 0 406746 264086 159080 91458 50890 27664 14830 7910 4206 2202 1108 526 246 132 98 66 34 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*10 + 1*18 + 1*21 + 1*22 + 1*34 + 1*46 + 2*66 + 1*96 + 1*98 + 1*132 + 1*152 + 1*202 + 1*246 + 1*316 + 1*426 + 1*526 + 1*600 + 1*898 + 1*1104 + 1*1108 + 1*1892 + 1*2086 +
1*2202 + 1*3986 + 1*4048 + 1*4206 + 1*7856 + 1*7910 + 1*8398 + 1*14830 + 1*14974 + 1*17694 + 1*27664 + 1*27932 + 1*37280 + 1*50890 + 1*51072 + 1*78546 + 1*91396 + 1*91458 + 1*158820 +
1*159080 + 1*165490 + 1*263786 + 1*264086 + 1*348674 + 1*406428 + 1*406746) +
4(8*0 + 3*1 + 2*3 + 1*7 + 2*15 + 3*17 + 1*30 + 1*31 + 1*43 + 1*58 + 1*65 + 1*75 + 1*91 + 2*137 + 1*195 + 1*289 + 1*297 + 1*359 + 1*609 + 2*632 + 1*1161 + 1*1249 + 1*1283 + 1*2215 + 1*2337 +
1*2703 + 1*4221 + 1*4271 + 1*5695 + 1*7746 + 1*7830 + 1*11999 + 1*13883 + 1*14051 + 1*24213 + 1*24351 + 1*25281 + 1*40293 + 1*40347 + 1*53265 + 2*62112) +
4(9*0 + 3*2 + 2*6 + 1*14 + 2*16 + 1*28 + 1*30 + 3*32 + 1*56 + 1*62 + 1*80 + 1*108 + 1*130 + 1*140 + 1*168 + 1*254 + 1*274 + 1*358 + 1*544 + 1*578 + 1*656 + 1*1144 + 1*1148 + 1*1218 + 1*2088 +
1*2236 + 1*2566 + 1*3926 + 1*4134 + 1*5406 + 1*7344 + 1*7440 + 1*11390 + 1*13204 + 1*13312 + 1*22932 + 1*23168 + 1*23998 + 1*38158 + 1*38390 + 1*50562 + 1*58848 + 1*59072) +
4(9*0 + 3*3 + 2*9 + 4*15 + 1*21 + 1*39 + 5*45 + 1*78 + 1*93 + 1*111 + 1*150 + 2*195 + 1*231 + 1*351 + 1*411 + 1*489 + 1*741 + 1*867 + 1*891 + 1*1536 + 1*1548 + 1*1827 + 1*2781 + 1*2961 +
1*3849 + 1*5133 + 1*5391 + 1*8109 + 1*9369 + 1*9507 + 1*16374 + 1*16446 + 1*17085 + 1*27147 + 1*27351 + 1*35997 + 1*41835 + 1*42117) +
4(9*0 + 3*4 + 2*12 + 3*14 + 2*28 + 2*42 + 1*48 + 5*56 + 1*60 + 1*96 + 1*124 + 1*136 + 1*184 + 1*240 + 1*260 + 1*280 + 1*428 + 1*548 + 1*588 + 1*888 + 1*1064 + 1*1156 + 1*1808 + 1*1832 + 1*2436 +
1*3240 + 1*3424 + 1*5132 + 1*5836 + 1*6108 + 1*10296 + 1*10472 + 1*10812 + 1*17232 + 1*17256 + 1*22780 + 1*26528 + 1*26600) +
4(9*0 + 3*5 + 3*13 + 2*15 + 1*35 + 3*39 + 1*55 + 4*65 + 1*75 + 1*78 + 2*91 + 1*110 + 1*130 + 2*155 + 1*210 + 1*275 + 1*315 + 1*325 + 1*485 + 1*655 + 1*685 + 1*985 + 1*1175 + 1*1445 + 1*1960 +
1*2000 + 1*3045 + 1*3465 + 1*3625 + 1*6035 + 1*6285 + 1*6415 + 1*10125 + 1*10335 + 1*15670 + 1*13515 + 1*15850) +
4(9*0 + 3*6 + 3*12 + 2*18 + 2*36 + 1*42 + 1*48 + 1*60 + 4*72 + 1*84 + 1*90 + 1*96 + 2*120 + 3*168 + 1*180 + 1*186 + 1*228 + 1*240 + 1*300 + 1*336 + 1*390 + 1*522 + 1*690 + 1*822 + 1*1032 +
1*1224 + 1*1734 + 1*1992 + 1*2052 + 1*3456 + 1*3564 + 1*3654 + 1*5730 + 1*5922 + 1*7698 + 1*8856 + 1*9096) +
4(9*0 + 3*7 + 3*11 + 2*21 + 2*33 + 1*49 + 1*55 + 1*63 + 5*77 + 1*105 + 1*110 + 1*126 + 1*143 + 1*165 + 1*175 + 1*198 + 1*217 + 1*231 + 1*238 + 1*275 + 1*315 + 1*341 + 1*343 + 1*385 + 1*407 +
1*455 + 1*539 + 1*693 + 1*959 + 1*1029 + 1*1211 + 1*1904 + 1*1988 + 1*2023 + 1*3213 + 1*3241 + 1*4263 + 1*4921 + 1*5019) +
4(9*0 + 3*8 + 3*10 + 2*24 + 2*30 + 1*56 + 1*60 + 1*64 + 1*70 + 4*80 + 2*120 + 1*128 + 1*150 + 1*160 + 1*176 + 1*220 + 1*240 + 1*248 + 1*280 + 1*300 + 1*310 + 1*320 + 1*336 + 1*470 + 1*510 +
1*520 + 1*536 + 1*650 + 1*664 + 1*720 + 1*800 + 1*976 + 1*1096 + 1*1136 + 1*1696 + 1*1808 + 1*2312 + 1*2656 + 1*2736) +
2(9*0 + 6*9 + 4*27 + 4*63 + 4*81 + 2*126 + 2*135 + 2*171 + 2*234 + 2*279 + 4*315 + 2*513 + 2*585 + 2*603 + 2*873 + 2*999 + 2*1233 + 2*1368 + 2*1512) +
2(55*0 + 2*17) +
17(57*0)
= 10902524 + 1665580 + 1581240 + 1126152 + 713560 + 425264 + 246072 + 143784 + 92504 + 38520 + 68
= 16935268
Value repetition frequencies = 4(50*1 + 2*2 + 1*3) +
4(33*1 + 5*2 + 2*3 + 1*8) +
4(38*1 + 2*2 + 2*3 + 1*9) +
4(32*1 + 2*2 + 1*3 + 1*4 + 1*5 + 1*9) +
4(31*1 + 3*2 + 2*3 + 1*5 + 1*9) +
4(29*1 + 3*2 + 3*3 + 1*4 + 1*9) +
4(29*1 + 3*2 + 3*3 + 1*4 + 1*9) +
4(33*1 + 2*2 + 2*3 + 1*5 + 1*9) +
4(32*1 + 3*2 + 2*3 + 1*4 + 1*9) +
2(13*2 + 4*4 + 1*6 + 1*9) +
2(1*2 + 1*55) +
17(1*57)
= 3249
Number of distinct row element sets = 12
Number of rows = 2*2 + 9*4 + 1*17
= 57
Number of distinct values = 323
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 21
Frequency 1393 12 24 20 20 12 20 16 12 20 16 12 20 12 16 32 8 16 12 16
Distinct values 22 24 27 28 30 31 32 33 34 35 36 39 42 43 45 46 48 49 55 56
Frequency 4 8 8 12 16 4 12 8 4 4 8 16 12 4 20 4 8 4 8 28
Distinct values 58 60 62 63 64 65 66 70 72 75 77 78 80 81 84 90 91 93 96 98
Frequency 4 12 4 12 4 20 8 4 16 8 20 8 20 8 4 4 12 4 12 4
Distinct values 105 108 110 111 120 124 126 128 130 132 135 136 137 140 143 150 152 155 160 165
Frequency 4 4 8 4 16 4 8 4 8 4 4 4 8 4 4 8 4 8 4 4
Distinct values 168 171 175 176 180 184 186 195 198 202 210 217 220 228 231 234 238 240 246 248
Frequency 16 4 4 4 4 4 4 12 4 4 4 4 4 4 8 4 4 12 4 4
Distinct values 254 260 274 275 279 280 289 297 300 310 315 316 320 325 336 341 343 351 358 359
Frequency 4 4 4 8 4 8 4 4 8 4 16 4 4 4 8 4 4 4 4 4
Distinct values 385 390 407 411 426 428 455 470 485 489 510 513 520 522 526 536 539 544 548 578
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 585 588 600 603 609 632 650 655 656 664 685 690 693 720 741 800 822 867 873 888
Frequency 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 891 898 959 976 985 999 1029 1032 1064 1096 1104 1108 1136 1144 1148 1156 1161 1175 1211 1218
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 1224 1233 1249 1283 1368 1445 1512 1536 1548 1696 1734 1808 1827 1832 1892 1904 1960 1988 1992 2000
Frequency 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4
Distinct values 2023 2052 2086 2088 2202 2215 2236 2312 2337 2436 2566 2656 2703 2736 2781 2961 3045 3213 3240 3241
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 3424 3456 3465 3564 3625 3654 3849 3926 3986 4048 4134 4206 4221 4263 4271 4921 5019 5132 5133 5391
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 5406 5695 5730 5836 5922 6035 6108 6285 6415 7344 7440 7698 7746 7830 7856 7910 8109 8398 8856 9096
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 9369 9507 10125 10296 10335 10472 10812 11390 11999 13204 13312 13515 13883 14051 14830 14974 15670 15850 16374 16446
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 17085 17232 17256 17694 22780 22932 23168 23998 24213 24351 25281 26528 26600 27147 27351 27664 27932 35997 37280 38158
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 38390 40293 40347 41835 42117 50562 50890 51072 53265 58848 59072 62112 78546 91396 91458 158820 159080 165490 263786 264086
Frequency 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4
Distinct values 348674 406428 406746
Frequency 4 4 4
Sum of distinct value frequencies = 259*4 + 25*8 + 15*12 + 11*16 + 9*20 + 1*24 + 1*28 + 1*32 + 1*1393
= 3249
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 30*48 + 4*49 + 4*54
= 1856
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1336
Number of possible SN-EN pairs with SN != EN = 56*57
= 3192
a = 20, b = 3
L C
3 8
4 16
5 32
6 44
7 152
8 184
9 480
10 740
11 1368
12 2036
13 3552
14 5624
15 9676
16 15656
17 26140
18 42292
19 69584
20 113148
21 185408
22 301984
23 492440
24 798184
25 1270952
26 1989644
27 2785800
28 3960732
29 4192892
30 5161068
31 4049588
32 3991544
33 2547864
34 1837480
35 986944
36 510500
37 217580
38 80012
39 24380
40 5728
41 1112
42 60
Total 35682628
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
L
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0
0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0
7 1 1 1 0 13 0 0 0 0 0 0 0 0 0 0 13 0 1 1 1
2 2 4 8 4 8 4 4 4 4 4 4 4 4 8 4 8 4 2 2
1 1 1 0 13 0 0 0 0 0 0 0 0 0 0 13 0 1 1 1
8 0 0 0 3 0 17 0 0 0 0 0 0 0 0 17 0 3 0 0 0
2 2 2 4 18 4 8 4 4 4 4 4 4 8 4 18 4 2 2 2
0 0 0 3 0 17 0 0 0 0 0 0 0 0 17 0 3 0 0 0
9 3 3 4 4 14 4 25 4 4 4 4 4 4 25 4 14 4 4 3 3
4 4 4 6 8 40 8 12 8 8 8 8 12 8 40 8 6 4 4 4
3 3 4 4 14 4 25 4 4 4 4 4 4 25 4 14 4 4 3 3
10 4 4 4 9 8 36 8 33 8 8 8 8 33 8 36 8 9 4 4 4
4 4 4 4 8 8 66 8 12 8 8 12 8 66 8 8 4 4 4 4
4 4 4 9 8 36 8 33 8 8 8 8 33 8 36 8 9 4 4 4
11 9 10 11 10 22 18 82 18 47 18 18 47 18 82 18 22 10 11 10 9
6 6 6 6 8 18 12 104 12 16 16 12 104 12 18 8 6 6 6 6
9 10 11 10 22 18 82 18 47 18 18 47 18 82 18 22 10 11 10 9
12 12 12 12 17 12 34 24 150 24 57 57 24 150 24 34 12 17 12 12 12
10 10 10 10 10 16 46 20 154 24 24 154 20 46 16 10 10 10 10 10
12 12 12 17 12 34 24 150 24 57 57 24 150 24 34 12 17 12 12 12
13 21 22 24 23 34 28 71 44 266 81 81 266 44 71 28 34 23 24 22 21
20 20 20 20 20 22 36 122 44 224 224 44 122 36 22 20 20 20 20 20
21 22 24 23 34 28 71 44 266 81 81 266 44 71 28 34 23 24 22 21
14 32 33 33 38 34 52 46 141 107 426 426 107 141 46 52 34 38 33 33 32
36 36 36 36 36 36 44 72 282 314 314 282 72 44 36 36 36 36 36 36
32 33 33 38 34 52 46 141 107 426 426 107 141 46 52 34 38 33 33 32
15 57 62 64 64 75 70 111 147 323 674 674 323 147 111 70 75 64 64 62 57
62 62 62 62 62 62 68 90 428 586 586 428 90 68 62 62 62 62 62 62
57 62 64 64 75 70 111 147 323 674 674 323 147 111 70 75 64 64 62 57
16 96 103 104 109 105 124 161 203 974 681 681 974 203 161 124 105 109 104 103 96
102 102 102 102 102 106 102 494 190 1106 1106 190 494 102 106 102 102 102 102 102
96 103 104 109 105 124 161 203 974 681 681 974 203 161 124 105 109 104 103 96
17 167 180 186 186 198 246 236 1318 408 1375 1375 408 1318 236 246 198 186 186 180 167
168 168 168 168 172 168 632 170 1830 426 426 1830 170 632 168 172 168 168 168 168
167 180 186 186 198 246 236 1318 408 1375 1375 408 1318 236 246 198 186 186 180 167
18 280 297 304 310 363 325 1806 402 2437 736 736 2437 402 1806 325 363 310 304 297 280
280 280 280 284 280 834 280 3002 288 818 818 288 3002 280 834 280 284 280 280 280
280 297 304 310 363 325 1806 402 2437 736 736 2437 402 1806 325 363 310 304 297 280
19 473 502 516 581 532 2488 571 4451 697 1162 1162 697 4451 571 2488 532 581 516 502 473
474 474 478 474 1126 474 4784 470 1802 290 290 1802 470 4784 474 1126 474 478 474 474
473 502 516 581 532 2488 571 4451 697 1162 1162 697 4451 571 2488 532 581 516 502 473
20 792 839 921 868 3383 884 7746 918 2322 731 731 2322 918 7746 884 3383 868 921 839 792
806 810 806 1564 806 7328 802 4136 506 202 202 506 4136 802 7328 806 1564 806 810 806
792 839 921 868 3383 884 7746 918 2322 731 731 2322 918 7746 884 3383 868 921 839 792
21 1337 1491 1452 4638 1480 12975 1472 5039 874 1068 1068 874 5039 1472 12975 1480 4638 1452 1491 1337
1372 1368 2240 1368 10874 1364 8790 996 614 66 66 614 996 8790 1364 10874 1368 2240 1368 1372
1337 1491 1452 4638 1480 12975 1472 5039 874 1068 1068 874 5039 1472 12975 1480 4638 1452 1491 1337
22 2329 2401 6384 2470 20884 2441 10708 1451 2068 672 672 2068 1451 10708 2441 20884 2470 6384 2401 2329
2312 3306 2312 15738 2308 17454 1860 1846 224 16 16 224 1846 1860 17454 2308 15738 2312 3306 2312
2329 2401 6384 2470 20884 2441 10708 1451 2068 672 672 2068 1451 10708 2441 20884 2470 6384 2401 2329
23 3817 8878 4152 32569 4148 22052 2752 4384 727 1075 1075 727 4384 2752 22052 4148 32569 4152 8878 3817
5022 3898 22360 3894 32696 3358 5140 658 84 2 2 84 658 5140 3358 32696 3894 22360 3898 5022
3817 8878 4152 32569 4148 22052 2752 4384 727 1075 1075 727 4384 2752 22052 4148 32569 4152 8878 3817
24 12258 6863 49385 7000 43499 5147 9427 1210 2040 680 680 2040 1210 9427 5147 43499 7000 49385 6863 12258
6570 31380 6566 58268 5934 13288 1698 352 18 0 0 18 352 1698 13288 5934 58268 6566 31380 6570
12258 6863 49385 7000 43499 5147 9427 1210 2040 680 680 2040 1210 9427 5147 43499 7000 49385 6863 12258
25 10891 73087 11774 82326 9466 20542 2566 4242 726 1081 1081 726 4242 2566 20542 9466 82326 11774 73087 10891
43766 11080 99498 10344 32026 3972 1286 100 2 0 0 2 100 1286 3972 32026 10344 99498 11080 43766
10891 73087 11774 82326 9466 20542 2566 4242 726 1081 1081 726 4242 2566 20542 9466 82326 11774 73087 10891
26 105386 19481 149630 16978 44599 5561 8891 1135 2054 681 681 2054 1135 8891 5561 44599 16978 149630 19481 105386
18712 163794 17864 72354 8612 4254 420 20 0 0 0 0 20 420 4254 8612 72354 17864 163794 18712
105386 19481 149630 16978 44599 5561 8891 1135 2054 681 681 2054 1135 8891 5561 44599 16978 149630 19481 105386
27 30953 261753 29820 95648 11920 18868 2252 4271 732 1081 1081 732 4271 2252 18868 11920 95648 29820 261753 30953
261324 30642 154168 17606 12976 1462 124 2 0 0 0 0 2 124 1462 12976 17606 154168 30642 261324
30953 261753 29820 95648 11920 18868 2252 4271 732 1081 1081 732 4271 2252 18868 11920 95648 29820 261753 30953
28 436306 50979 200433 24616 40227 4695 8904 1153 2055 681 681 2055 1153 8904 4695 40227 24616 200433 50979 436306
52294 311704 34394 36832 4426 596 22 0 0 0 0 0 0 22 596 4426 36832 34394 311704 52294
436306 50979 200433 24616 40227 4695 8904 1153 2055 681 681 2055 1153 8904 4695 40227 24616 200433 50979 436306
29 82717 403914 48820 86195 10116 18712 2276 4274 731 1080 1080 731 4274 2276 18712 10116 86195 48820 403914 82717
601434 64884 97854 12020 2438 144 2 0 0 0 0 0 0 2 144 2438 12020 97854 64884 601434
82717 403914 48820 86195 10116 18712 2276 4274 731 1080 1080 731 4274 2276 18712 10116 86195 48820 403914 82717
30 736258 91977 182008 21790 39190 4633 8915 1147 2054 681 681 2054 1147 8915 4633 39190 21790 182008 91977 736258
119172 244518 29924 8886 704 24 0 0 0 0 0 0 0 0 24 704 8886 29924 244518 119172
736258 91977 182008 21790 39190 4633 8915 1147 2054 681 681 2054 1147 8915 4633 39190 21790 182008 91977 736258
31 159273 351240 46040 79678 9492 18664 2256 4261 726 1078 1078 726 4261 2256 18664 9492 79678 46040 351240 159273
577376 69406 29596 2826 172 2 0 0 0 0 0 0 0 0 2 172 2826 29596 69406 577376
159273 351240 46040 79678 9492 18664 2256 4261 726 1078 1078 726 4261 2256 18664 9492 79678 46040 351240 159273
32 564602 91495 141568 18960 37036 4523 8824 1130 2047 680 680 2047 1130 8824 4523 37036 18960 141568 91495 564602
151894 91392 9794 936 26 0 0 0 0 0 0 0 0 0 0 26 936 9794 91392 151894
564602 91495 141568 18960 37036 4523 8824 1130 2047 680 680 2047 1130 8824 4523 37036 18960 141568 91495 564602
33 159023 198084 35470 61006 8902 16974 2171 4191 712 1072 1072 712 4191 2171 16974 8902 61006 35470 198084 159023
264018 30244 4262 196 2 0 0 0 0 0 0 0 0 0 0 2 196 4262 30244 264018
159023 198084 35470 61006 8902 16974 2171 4191 712 1072 1072 712 4191 2171 16974 8902 61006 35470 198084 159023
34 219366 56565 74932 15854 25569 4109 7610 1083 1993 672 672 1993 1083 7610 4109 25569 15854 74932 56565 219366
85044 17070 1092 28 0 0 0 0 0 0 0 0 0 0 0 0 28 1092 17070 85044
219366 56565 74932 15854 25569 4109 7610 1083 1993 672 672 1993 1083 7610 4109 25569 15854 74932 56565 219366
35 71137 67604 22348 27897 6988 10243 1922 3344 682 1021 1021 682 3344 1922 10243 6988 27897 22348 67604 71137
61912 4958 228 2 0 0 0 0 0 0 0 0 0 0 0 0 2 228 4958 61912
71137 67604 22348 27897 6988 10243 1922 3344 682 1021 1021 682 3344 1922 10243 6988 27897 22348 67604 71137
36 44886 21695 22277 8804 9739 2988 3883 938 1426 619 619 1426 938 3883 2988 9739 8804 22277 21695 44886
19322 1388 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30 1388 19322
44886 21695 22277 8804 9739 2988 3883 938 1426 619 619 1426 938 3883 2988 9739 8804 22277 21695 44886
37 13457 12906 7320 6766 3239 3200 1268 1408 567 644 644 567 1408 1268 3200 3239 6766 7320 12906 13457
6982 256 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 256 6982
13457 12906 7320 6766 3239 3200 1268 1408 567 644 644 567 1408 1268 3200 3239 6766 7320 12906 13457
38 4442 3841 3376 2174 1886 1101 978 541 494 354 354 494 541 978 1101 1886 2174 3376 3841 4442
1600 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 1600
4442 3841 3376 2174 1886 1101 978 541 494 354 354 494 541 978 1101 1886 2174 3376 3841 4442
39 961 1153 904 771 578 484 357 296 232 212 212 232 296 357 484 578 771 904 1153 961
292 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 292
961 1153 904 771 578 484 357 296 232 212 212 232 296 357 484 578 771 904 1153 961
40 163 223 198 173 147 127 110 98 90 86 86 90 98 110 127 147 173 198 223 163
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 34
163 223 198 173 147 127 110 98 90 86 86 90 98 110 127 147 173 198 223 163
41 19 32 31 28 27 28 28 28 28 28 28 28 28 28 28 27 28 31 32 19
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
19 32 31 28 27 28 28 28 28 28 28 28 28 28 28 27 28 31 32 19
42 0 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 0
Total 2661529 1727733 1040512 598573 333927 182395 98459 53455 30677 21201 21201 30677 53455 98459 182395 333927 598573 1040512 1727733 2661529
2282430 1083306 514170 244050 115858 55042 26234 12682 6506 4114 4114 6506 12682 26234 55042 115858 244050 514170 1083306 2282430
2661529 1727733 1040512 598573 333927 182395 98459 53455 30677 21201 21201 30677 53455 98459 182395 333927 598573 1040512 1727733 2661529
Grand total = 2*4114 + 2*6506 + 2*12682 + 4*21201 + 2*26234 + 4*30677 + 4*53455 + 2*55042 + 4*98459 + 2*115858 + 4*182395 + 2*244050 + 4*333927 + 2*514170 + 4*598573 + 4*1040512 + 2*1083306 + 4*1727733 + 2*2282430 + 4*2661529
= 35682628
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 12 12 12 12 12 12 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 12 12 12 12 12 12 12 12 12 11 7 5 90
11 158 9 14 17 23 24 24 24 24 24 24 24 24 24 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 24 24 24 24 24 24 24 24 24 23 17 14 9 158
12 265 11 17 22 25 33 34 34 34 34 34 34 34 34 33 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 33 34 34 34 34 34 34 34 34 33 25 22 17 11 265
13 445 21 31 36 46 53 63 64 64 64 64 64 64 63 53 46 36 31 21 445
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
445 21 31 36 46 53 63 64 64 64 64 64 64 63 53 46 36 31 21 445
14 741 34 46 55 60 76 89 101 102 102 102 102 101 89 76 60 55 46 34 741
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
741 34 46 55 60 76 89 101 102 102 102 102 101 89 76 60 55 46 34 741
15 1248 63 85 95 107 120 152 173 187 188 188 187 173 152 120 107 95 85 63 1248
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
1248 63 85 95 107 120 152 173 187 188 188 187 173 152 120 107 95 85 63 1248
16 2107 104 139 154 163 181 202 262 293 309 309 293 262 202 181 163 154 139 104 2107
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2107 104 139 154 163 181 202 262 293 309 309 293 262 202 181 163 154 139 104 2107
17 3571 177 241 263 280 295 335 374 478 520 520 478 374 335 295 280 263 241 177 3571
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
3571 177 241 263 280 295 335 374 478 520 520 478 374 335 295 280 263 241 177 3571
18 6039 290 395 433 448 470 493 571 643 791 791 643 571 493 470 448 433 395 290 6039
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6039 290 395 433 448 470 493 571 643 791 791 643 571 493 470 448 433 395 290 6039
19 10202 489 667 731 760 780 822 870 1006 1068 1068 1006 870 822 780 760 731 667 489 10202
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
10202 489 667 731 760 780 822 870 1006 1068 1068 1006 870 822 780 760 731 667 489 10202
20 17211 822 1113 1221 1259 1287 1313 1369 1375 1317 1317 1375 1369 1313 1287 1259 1221 1113 822 17211
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17211 822 1113 1221 1259 1287 1313 1369 1375 1317 1317 1375 1369 1313 1287 1259 1221 1113 822 17211
21 29041 1397 1887 2065 2136 2167 2188 2128 1778 1564 1564 1778 2128 2188 2167 2136 2065 1887 1397 29041
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
29041 1397 1887 2065 2136 2167 2188 2128 1778 1564 1564 1778 2128 2188 2167 2136 2065 1887 1397 29041
22 49013 2362 3185 3479 3586 3609 3509 2889 2319 1545 1545 2319 2889 3509 3609 3586 3479 3185 2362 49013
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
49013 2362 3185 3479 3586 3609 3509 2889 2319 1545 1545 2319 2889 3509 3609 3586 3479 3185 2362 49013
23 82685 3995 5393 5882 6037 5954 5085 4098 2264 1716 1716 2264 4098 5085 5954 6037 5882 5393 3995 82685
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
82685 3995 5393 5882 6037 5954 5085 4098 2264 1716 1716 2264 4098 5085 5954 6037 5882 5393 3995 82685
24 139047 6736 9098 9892 10003 8928 7419 4083 2745 1595 1595 2745 4083 7419 8928 10003 9892 9098 6736 139047
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
139047 6736 9098 9892 10003 8928 7419 4083 2745 1595 1595 2745 4083 7419 8928 10003 9892 9098 6736 139047
25 228274 11364 15326 16513 15498 13415 7894 5293 2430 1730 1730 2430 5293 7894 13415 15498 16513 15326 11364 228274
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
228274 11364 15326 16513 15498 13415 7894 5293 2430 1730 1730 2430 5293 7894 13415 15498 16513 15326 11364 228274
26 368170 19137 25633 26119 23744 15157 10476 4573 2807 1595 1595 2807 4573 10476 15157 23744 26119 25633 19137 368170
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
368170 19137 25633 26119 23744 15157 10476 4573 2807 1595 1595 2807 4573 10476 15157 23744 26119 25633 19137 368170
27 514465 32066 41127 40724 28515 20616 9227 5544 2439 1726 1726 2439 5544 9227 20616 28515 40724 41127 32066 514465
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
514465 32066 41127 40724 28515 20616 9227 5544 2439 1726 1726 2439 5544 9227 20616 28515 40724 41127 32066 514465
28 744195 51575 64801 51306 39447 18542 11311 4620 2797 1589 1589 2797 4620 11311 18542 39447 51306 64801 51575 744195
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
744195 51575 64801 51306 39447 18542 11311 4620 2797 1589 1589 2797 4620 11311 18542 39447 51306 64801 51575 744195
29 732772 81128 83935 71902 36392 23079 9380 5501 2418 1715 1715 2418 5501 9380 23079 36392 71902 83935 81128 732772
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
732772 81128 83935 71902 36392 23079 9380 5501 2418 1715 1715 2418 5501 9380 23079 36392 71902 83935 81128 732772
30 918081 103125 117671 67004 45565 18845 11124 4517 2762 1573 1573 2762 4517 11124 18845 45565 67004 117671 103125 918081
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
918081 103125 117671 67004 45565 18845 11124 4517 2762 1573 1573 2762 4517 11124 18845 45565 67004 117671 103125 918081
31 605171 141496 106005 83372 35916 22159 8913 5324 2353 1687 1687 2353 5324 8913 22159 35916 83372 106005 141496 605171
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
605171 141496 106005 83372 35916 22159 8913 5324 2353 1687 1687 2353 5324 8913 22159 35916 83372 106005 141496 605171
32 618379 115209 128081 59978 40895 16633 10304 4226 2653 1528 1528 2653 4226 10304 16633 40895 59978 128081 115209 618379
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
618379 115209 128081 59978 40895 16633 10304 4226 2653 1528 1528 2653 4226 10304 16633 40895 59978 128081 115209 618379
33 299690 132588 79097 64216 26848 18375 7543 4834 2169 1605 1605 2169 4834 7543 18375 26848 64216 79097 132588 299690
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
299690 132588 79097 64216 26848 18375 7543 4834 2169 1605 1605 2169 4834 7543 18375 26848 64216 79097 132588 299690
34 223869 70509 76781 34650 27011 11281 8102 3424 2353 1390 1390 2353 3424 8102 11281 27011 34650 76781 70509 223869
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
223869 70509 76781 34650 27011 11281 8102 3424 2353 1390 1390 2353 3424 8102 11281 27011 34650 76781 70509 223869
35 86501 60026 34923 29812 13368 10851 4635 3567 1684 1368 1368 1684 3567 4635 10851 13368 29812 34923 60026 86501
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
86501 60026 34923 29812 13368 10851 4635 3567 1684 1368 1368 1684 3567 4635 10851 13368 29812 34923 60026 86501
36 42961 24307 23807 12418 10487 4947 4176 1892 1612 1018 1018 1612 1892 4176 4947 10487 12418 23807 24307 42961
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
42961 24307 23807 12418 10487 4947 4176 1892 1612 1018 1018 1612 1892 4176 4947 10487 12418 23807 24307 42961
37 13088 12840 8599 7250 4094 3471 1798 1574 862 818 818 862 1574 1798 3471 4094 7250 8599 12840 13088
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
13088 12840 8599 7250 4094 3471 1798 1574 862 818 818 862 1574 1798 3471 4094 7250 8599 12840 13088
38 4047 3981 3539 2396 2007 1267 1074 660 582 450 450 582 660 1074 1267 2007 2396 3539 3981 4047
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4047 3981 3539 2396 2007 1267 1074 660 582 450 450 582 660 1074 1267 2007 2396 3539 3981 4047
39 871 1164 937 798 604 512 384 324 260 240 240 260 324 384 512 604 798 937 1164 871
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
871 1164 937 798 604 512 384 324 260 240 240 260 324 384 512 604 798 937 1164 871
40 149 225 201 174 151 132 114 102 94 90 90 94 102 114 132 151 174 201 225 149
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
149 225 201 174 151 132 114 102 94 90 90 94 102 114 132 151 174 201 225 149
41 18 32 31 28 28 28 28 28 28 28 28 28 28 28 28 28 28 31 32 18
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
18 32 31 28 28 28 28 28 28 28 28 28 28 28 28 28 28 31 32 18
42 0 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 0
Total 5742689 877295 832824 593029 375529 223313 128237 73069 43641 31013 31013 43641 73069 128237 223313 375529 593029 832824 877295 5742689
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 36
5742689 877295 832824 593029 375529 223313 128237 73069 43641 31013 31013 43641 73069 128237 223313 375529 593029 832824 877295 5742689
Grand total = 2*36 + 4*31013 + 4*43641 + 4*73069 + 4*128237 + 4*223313 + 4*375529 + 4*593029 + 4*832824 + 4*877295 + 4*5742689
= 35682628
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
L
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 0 0 0 0 0 0 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 0 0 0 0 0 0 0 0 0 9 5 7 11
12 22 18 12 4 0 0 0 0 0 0 0 0 0 0 4 12 18 22 12
11 7 5 9 0 0 0 0 0 0 0 0 0 0 0 0 9 5 7 11
7 25 24 23 21 23 10 10 10 10 10 10 10 10 10 10 23 21 23 24 25
26 38 40 32 20 12 8 8 8 8 8 8 8 8 12 20 32 40 38 26
25 24 23 21 23 10 10 10 10 10 10 10 10 10 10 23 21 23 24 25
8 32 27 24 31 28 27 10 10 10 10 10 10 10 10 27 28 31 24 27 32
36 62 50 48 46 24 16 12 12 12 12 12 12 16 24 46 48 50 62 36
32 27 24 31 28 27 10 10 10 10 10 10 10 10 27 28 31 24 27 32
9 68 67 72 93 92 76 71 50 50 50 50 50 50 71 76 92 93 72 67 68
76 118 96 104 100 96 56 48 44 44 44 44 48 56 96 100 104 96 118 76
68 67 72 93 92 76 71 50 50 50 50 50 50 71 76 92 93 72 67 68
10 108 100 99 135 156 154 112 103 78 78 78 78 103 112 154 156 135 99 100 108
120 208 176 158 182 180 162 96 88 84 84 88 96 162 180 182 158 176 208 120
108 100 99 135 156 154 112 103 78 78 78 78 103 112 154 156 135 99 100 108
11 201 191 194 252 302 314 308 222 209 180 180 209 222 308 314 302 252 194 191 201
218 358 308 284 304 348 326 280 180 172 172 180 280 326 348 304 284 308 358 218
201 191 194 252 302 314 308 222 209 180 180 209 222 308 314 302 252 194 191 201
12 320 289 280 367 422 475 481 474 318 301 301 318 474 481 475 422 367 280 289 320
346 590 508 466 474 530 594 524 434 296 296 434 524 594 530 474 466 508 590 346
320 289 280 367 422 475 481 474 318 301 301 318 474 481 475 422 367 280 289 320
13 557 518 513 661 770 852 912 893 882 659 659 882 893 912 852 770 661 513 518 557
600 992 856 802 810 898 990 1060 894 752 752 894 1060 990 898 810 802 856 992 600
557 518 513 661 770 852 912 893 882 659 659 882 893 912 852 770 661 513 518 557
14 910 842 816 1053 1198 1332 1447 1530 1482 1482 1482 1482 1530 1447 1332 1198 1053 816 842 910
984 1656 1414 1340 1384 1476 1624 1762 1826 1718 1718 1826 1762 1624 1476 1384 1340 1414 1656 984
910 842 816 1053 1198 1332 1447 1530 1482 1482 1482 1482 1530 1447 1332 1198 1053 816 842 910
15 1566 1485 1472 1876 2141 2341 2593 2826 2954 3295 3295 2954 2826 2593 2341 2141 1876 1472 1485 1566
1696 2824 2412 2284 2410 2598 2796 3070 3536 3846 3846 3536 3070 2796 2598 2410 2284 2412 2824 1696
1566 1485 1472 1876 2141 2341 2593 2826 2954 3295 3295 2954 2826 2593 2341 2141 1876 1472 1485 1566
16 2618 2468 2428 3103 3496 3803 4154 4618 5772 5993 5993 5772 4618 4154 3803 3496 3103 2428 2468 2618
2840 4774 4070 3844 4046 4462 4782 5464 6372 7688 7688 6372 5464 4782 4462 4046 3844 4070 4774 2840
2618 2468 2428 3103 3496 3803 4154 4618 5772 5993 5993 5772 4618 4154 3803 3496 3103 2428 2468 2618
17 4472 4238 4206 5361 6062 6589 7147 8909 9840 11588 11588 9840 8909 7147 6589 6062 5361 4206 4238 4472
4846 8110 6938 6532 6876 7578 8692 9774 12330 13690 13690 12330 9774 8692 7578 6876 6532 6938 8110 4846
4472 4238 4206 5361 6062 6589 7147 8909 9840 11588 11588 9840 8909 7147 6589 6062 5361 4206 4238 4472
18 7514 7067 6968 8903 10085 10899 13170 14441 18064 19171 19171 18064 14441 13170 10899 10085 8903 6968 7067 7514
8138 13664 11690 11002 11506 13258 15072 19270 21358 23106 23106 21358 19270 15072 13258 11506 11002 11690 13664 8138
7514 7067 6968 8903 10085 10899 13170 14441 18064 19171 19171 18064 14441 13170 10899 10085 8903 6968 7067 7514
19 12731 11993 11853 15198 17207 20532 22268 28364 30166 31689 31689 30166 28364 22268 20532 17207 15198 11853 11993 12731
13778 23078 19766 18612 20106 22830 29818 33886 37704 37468 37468 37704 33886 29818 22830 20106 18612 19766 23078 13778
12731 11993 11853 15198 17207 20532 22268 28364 30166 31689 31689 30166 28364 22268 20532 17207 15198 11853 11993 12731
20 21426 20141 19909 25467 31330 34283 44322 46795 49980 50515 50515 49980 46795 44322 34283 31330 25467 19909 20141 21426
23190 38890 33286 32130 34536 45046 52386 60978 61424 61278 61278 61424 60978 52386 45046 34536 32130 33286 38890 23190
21426 20141 19909 25467 31330 34283 44322 46795 49980 50515 50515 49980 46795 44322 34283 31330 25467 19909 20141 21426
21 36219 34191 33797 46390 53017 70054 74200 81017 81454 81208 81208 81454 81017 74200 70054 53017 46390 33797 34191 36219
39208 65692 57088 55074 68054 80160 96764 99750 101428 100472 100472 101428 99750 96764 80160 68054 55074 57088 65692 39208
36219 34191 33797 46390 53017 70054 74200 81017 81454 81208 81208 81454 81017 74200 70054 53017 46390 33797 34191 36219
22 61157 57663 60916 78062 108286 116299 131023 132255 131339 128978 128978 131339 132255 131023 116299 108286 78062 60916 57663 61157
66142 111874 97242 106448 121292 151982 160292 165176 163904 165516 165516 163904 165176 160292 151982 121292 106448 97242 111874 66142
61157 57663 60916 78062 108286 116299 131023 132255 131339 128978 128978 131339 132255 131023 116299 108286 78062 60916 57663 61157
23 103210 102261 102969 161282 180483 212134 215676 215591 210314 207990 207990 210314 215591 215676 212134 180483 161282 102969 102261 103210
112804 189892 182678 189308 235514 254952 268830 266350 268612 270300 270300 268612 266350 268830 254952 235514 189308 182678 189892 112804
103210 102261 102969 161282 180483 212134 215676 215591 210314 207990 207990 210314 215591 215676 212134 180483 161282 102969 102261 103210
24 179397 172067 216929 267887 338160 348870 351904 342764 337821 334120 334120 337821 342764 351904 348870 338160 267887 216929 172067 179397
189908 343358 320544 372226 398420 432222 431470 435174 436884 438164 438164 436884 435174 431470 432222 398420 372226 320544 343358 189908
179397 172067 216929 267887 338160 348870 351904 342764 337821 334120 334120 337821 342764 351904 348870 338160 267887 216929 172067 179397
25 290608 344789 355221 514951 552140 569334 553991 544175 535361 533273 533273 535361 544175 553991 569334 552140 514951 355221 344789 290608
343374 581626 615444 623312 674812 679680 691074 695322 697480 697090 697090 697480 695322 691074 679680 674812 623312 615444 581626 343374
290608 344789 355221 514951 552140 569334 553991 544175 535361 533273 533273 535361 544175 553991 569334 552140 514951 355221 344789 290608
26 557421 555772 712931 830342 901051 885163 865961 845990 841043 838930 838930 841043 845990 865961 885163 901051 830342 712931 555772 557421
557184 1073190 1019762 1063450 1047922 1073794 1084716 1093516 1093708 1088922 1088922 1093708 1093516 1084716 1073794 1047922 1063450 1019762 1073190 557184
557421 555772 712931 830342 901051 885163 865961 845990 841043 838930 838930 841043 845990 865961 885163 901051 830342 712931 555772 557421
27 729606 1021712 1062314 1282537 1294182 1266194 1221422 1207906 1202642 1204978 1204978 1202642 1207906 1221422 1266194 1294182 1282537 1062314 1021712 729606
976886 1546182 1547780 1450310 1473708 1504240 1533950 1539588 1527750 1520920 1520920 1527750 1539588 1533950 1504240 1473708 1450310 1547780 1546182 976886
729606 1021712 1062314 1282537 1294182 1266194 1221422 1207906 1202642 1204978 1204978 1202642 1207906 1221422 1266194 1294182 1282537 1062314 1021712 729606
28 1448653 1501538 1704236 1854549 1868668 1793356 1755048 1734599 1735625 1735566 1735566 1735625 1734599 1755048 1793356 1868668 1854549 1704236 1501538 1448653
1430702 2509532 2208660 2102712 2081302 2153020 2186076 2178702 2170774 2165092 2165092 2170774 2178702 2186076 2153020 2081302 2102712 2208660 2509532 1430702
1448653 1501538 1704236 1854549 1868668 1793356 1755048 1734599 1735625 1735566 1735566 1735625 1734599 1755048 1793356 1868668 1854549 1704236 1501538 1448653
29 1373767 1967781 2014528 2136802 2038619 1968925 1921649 1919783 1914392 1912474 1912474 1914392 1919783 1921649 1968925 2038619 2136802 2014528 1967781 1373767
1872446 2471910 2275236 2128648 2235266 2310868 2301298 2286062 2282706 2295054 2295054 2282706 2286062 2301298 2310868 2235266 2128648 2275236 2471910 1872446
1373767 1967781 2014528 2136802 2038619 1968925 1921649 1919783 1914392 1912474 1912474 1914392 1919783 1921649 1968925 2038619 2136802 2014528 1967781 1373767
30 2329501 2513502 2624040 2634042 2562109 2445561 2417515 2406588 2408069 2402949 2402949 2408069 2406588 2417515 2445561 2562109 2634042 2624040 2513502 2329501
2378290 3357646 2722976 2616166 2752018 2833130 2833952 2804958 2809794 2819338 2819338 2809794 2804958 2833952 2833130 2752018 2616166 2722976 3357646 2378290
2329501 2513502 2624040 2634042 2562109 2445561 2417515 2406588 2408069 2402949 2402949 2408069 2406588 2417515 2445561 2562109 2634042 2624040 2513502 2329501
31 1799657 2365596 2282682 2229379 2059502 1997636 1962572 1963838 1954354 1951829 1951829 1954354 1963838 1962572 1997636 2059502 2229379 2282682 2365596 1799657
2229964 2194640 2002458 2035792 2176726 2216920 2186090 2194758 2197780 2199396 2199396 2197780 2194758 2186090 2216920 2176726 2035792 2002458 2194640 2229964
1799657 2365596 2282682 2229379 2059502 1997636 1962572 1963838 1954354 1951829 1951829 1954354 1963838 1962572 1997636 2059502 2229379 2282682 2365596 1799657
32 2159441 2369809 2389460 2223558 2119440 2014134 2011319 1999247 1996643 1990658 1990658 1996643 1999247 2011319 2014134 2119440 2223558 2389460 2369809 2159441
2266464 2317860 1847096 1946232 2165144 2158742 2152072 2146082 2159154 2158440 2158440 2159154 2146082 2152072 2158742 2165144 1946232 1847096 2317860 2266464
2159441 2369809 2389460 2223558 2119440 2014134 2011319 1999247 1996643 1990658 1990658 1996643 1999247 2011319 2014134 2119440 2223558 2389460 2369809 2159441
33 1492948 1772057 1617807 1510655 1368514 1341966 1312910 1311834 1301812 1300874 1300874 1301812 1311834 1312910 1341966 1368514 1510655 1617807 1772057 1492948
1675872 1143500 1113386 1269578 1336836 1369130 1355670 1370732 1369704 1372594 1372594 1369704 1370732 1355670 1369130 1336836 1269578 1113386 1143500 1675872
1492948 1772057 1617807 1510655 1368514 1341966 1312910 1311834 1301812 1300874 1300874 1301812 1311834 1312910 1341966 1368514 1510655 1617807 1772057 1492948
34 1195557 1290275 1268708 1115273 1055234 994332 999972 983870 982126 978616 978616 982126 983870 999972 994332 1055234 1115273 1268708 1290275 1195557
1257044 821882 721248 858326 984740 952134 974798 975476 983156 980430 980430 983156 975476 974798 952134 984740 858326 721248 821882 1257044
1195557 1290275 1268708 1115273 1055234 994332 999972 983870 982126 978616 978616 982126 983870 999972 994332 1055234 1115273 1268708 1290275 1195557
35 708656 778230 700182 638150 572373 566864 547539 547423 540049 540027 540027 540049 547423 547539 566864 572373 638150 700182 778230 708656
750118 328862 364316 469236 486994 514186 509336 523512 521802 524172 524172 521802 523512 509336 514186 486994 469236 364316 328862 750118
708656 778230 700182 638150 572373 566864 547539 547423 540049 540027 540027 540049 547423 547539 566864 572373 638150 700182 778230 708656
36 395707 412218 393557 339288 319906 300467 302031 292674 293054 290807 290807 293054 292674 302031 300467 319906 339288 393557 412218 395707
408938 146532 166256 221814 254296 247380 265642 262816 268094 267814 267814 268094 262816 265642 247380 254296 221814 166256 146532 408938
395707 412218 393557 339288 319906 300467 302031 292674 293054 290807 290807 293054 292674 302031 300467 319906 339288 393557 412218 395707
37 182061 188329 172154 154539 140018 138177 132187 131951 129122 129260 129260 129122 131951 132187 138177 140018 154539 172154 188329 182061
186586 43980 64216 91384 96094 105804 106162 111788 110904 112716 112716 110904 111788 106162 105804 96094 91384 64216 43980 186586
182061 188329 172154 154539 140018 138177 132187 131951 129122 129260 129260 129122 131951 132187 138177 140018 154539 172154 188329 182061
38 71125 71409 67216 59155 55557 52898 52218 50415 50351 49735 49735 50351 50415 52218 52898 55557 59155 67216 71409 71125
72138 11342 20314 29532 33556 35280 38642 38614 40422 40230 40230 40422 38614 38642 35280 33556 29532 20314 11342 72138
71125 71409 67216 59155 55557 52898 52218 50415 50351 49735 49735 50351 50415 52218 52898 55557 59155 67216 71409 71125
39 22676 22580 21212 19217 17941 17491 16836 16580 16268 16188 16188 16268 16580 16836 17491 17941 19217 21212 22580 22676
22852 2134 5170 7774 8666 9988 10496 11224 11448 11680 11680 11448 11224 10496 9988 8666 7774 5170 2134 22852
22676 22580 21212 19217 17941 17491 16836 16580 16268 16188 16188 16268 16580 16836 17491 17941 19217 21212 22580 22676
40 5585 5427 5180 4759 4517 4400 4256 4184 4112 4088 4088 4112 4184 4256 4400 4517 4759 5180 5427 5585
5604 196 976 1476 1712 2028 2188 2380 2460 2524 2524 2460 2380 2188 2028 1712 1476 976 196 5604
5585 5427 5180 4759 4517 4400 4256 4184 4112 4088 4088 4112 4184 4256 4400 4517 4759 5180 5427 5585
41 1108 1077 1049 987 962 942 926 914 906 902 902 906 914 926 942 962 987 1049 1077 1108
1110 4 124 180 232 272 304 328 344 352 352 344 328 304 272 232 180 124 4 1110
1108 1077 1049 987 962 942 926 914 906 902 902 906 914 926 942 962 987 1049 1077 1108
42 60 60 58 56 56 56 56 56 56 56 56 56 56 56 56 56 56 58 60 60
60 0 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 0 60
60 60 58 56 56 56 56 56 56 56 56 56 56 56 56 56 56 58 60 60
Total 15196694 17597812 17856013 18164390 17684047 17186940 16948216 16842899 16786728 16758527 16758527 16786728 16842899 16948216 17186940 17684047 18164390 17856013 17597812 15196694
16900614 19357246 17434616 17716640 18716116 19185256 19307152 19338548 19364526 19381386 19381386 19364526 19338548 19307152 19185256 18716116 17716640 17434616 19357246 16900614
15196694 17597812 17856013 18164390 17684047 17186940 16948216 16842899 16786728 16758527 16758527 16786728 16842899 16948216 17186940 17684047 18164390 17856013 17597812 15196694
Grand total = 4*15196694 + 4*16758527 + 4*16786728 + 4*16842899 + 2*16900614 + 4*16948216 + 4*17186940 + 2*17434616 + 4*17597812 + 4*17684047 + 2*17716640 + 4*17856013 + 4*18164390 + 2*18716116 + 2*19185256 + 2*19307152 +
2*19338548 + 2*19357246 + 2*19364526 + 2*19381386
= 1057493264
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
EN
0 0 0 36 70 104 140 262 564 1196 2392 4600 8722 16524 31240 58466 107472 192824 335092 556204 856702 0 2 2 4 10 22 46 96 202 426 898
1892 3986 8398 17694 37280 78546 165490 348674 734628 19 2 4 22 70 162 338 644 1190 2262 4424 8666 16698 31558 58670 107352 192434 334698 555980 856590
1 0 0 0 18 3 18 32 98 211 390 690 1278 2467 4770 9004 16518 29507 51158 84886 130762 18 0 1 1 1 3 7 15 31 65 137
289 609 1283 2703 5695 11999 25281 53265 112225 0 0 0 0 16 46 62 80 147 322 692 1380 2607 4822 8890 16300 29347 51162 85016 130968
2 34 0 0 0 34 6 34 60 182 390 718 1264 2322 4430 8442 15660 28102 48702 80694 124224 17 17 0 2 2 2 6 14 30 62 130
274 578 1218 2566 5406 11390 23998 50562 106530 0 0 0 0 0 30 86 116 150 274 594 1264 2498 4674 8542 15492 27766 48426 80586 124224
3 48 48 0 0 0 48 9 48 84 252 537 984 1722 3132 5889 11016 19968 34752 57585 88608 16 16 16 0 3 3 3 9 21 45 93
195 411 867 1827 3849 8109 17085 35997 75843 16 0 0 0 0 0 42 120 162 210 381 816 1716 3354 6201 11160 19806 34398 57237 88272
4 60 45 60 0 0 0 60 12 60 104 308 652 1188 2064 3708 6844 12492 21928 36468 56156 45 15 15 15 0 4 4 4 12 28 60
124 260 548 1156 2436 5132 10812 22780 47996 60 30 0 0 0 0 0 52 148 200 260 468 988 2048 3948 7188 12676 21832 36196 55780
5 84 70 42 70 0 0 0 70 15 70 120 350 735 1330 2290 4050 7295 12870 21540 33250 98 42 14 14 14 0 5 5 5 15 35
75 155 325 685 1445 3045 6415 13515 28475 140 98 42 0 0 0 0 0 60 170 230 300 535 1110 2260 4280 7635 13090 21570 33160
6 182 104 78 39 78 0 0 0 78 18 78 132 378 786 1410 2400 4158 7242 12150 18804 195 91 39 13 13 13 0 6 6 6 18
42 90 186 390 822 1734 3654 7698 16218 260 182 130 52 0 0 0 0 0 66 186 252 330 582 1182 2352 4350 7542 12402 19020
7 420 252 120 84 36 84 0 0 0 84 21 84 140 392 805 1428 2394 4032 6685 10332 372 180 84 36 12 12 12 0 7 7 7
21 49 105 217 455 959 2023 4263 8981 444 300 216 156 60 0 0 0 0 0 70 196 266 350 609 1204 2324 4158 6909 10612
8 880 561 308 132 88 33 88 0 0 0 88 24 88 144 392 792 1384 2272 3672 5624 715 341 165 77 33 11 11 11 0 8 8
8 24 56 120 248 520 1096 2312 4872 792 517 330 242 176 66 0 0 0 0 0 72 200 272 360 616 1176 2176 3704 5736
9 1680 1110 670 350 140 90 30 90 0 0 0 90 27 90 144 378 747 1278 2034 3078 1370 650 310 150 70 30 10 10 10 0 9
9 9 27 63 135 279 585 1233 2601 1520 970 570 350 260 190 70 0 0 0 0 0 72 198 270 360 603 1098 1908 2988
10 3078 2034 1278 747 378 144 90 27 90 0 0 0 90 30 90 140 350 670 1110 1680 2601 1233 585 279 135 63 27 9 9 9 0
10 10 10 30 70 150 310 650 1370 2988 1908 1098 603 360 270 198 72 0 0 0 0 0 70 190 260 350 570 970 1520
11 5624 3672 2272 1384 792 392 144 88 24 88 0 0 0 88 33 88 132 308 561 880 4872 2312 1096 520 248 120 56 24 8 8 8
0 11 11 11 33 77 165 341 715 5736 3704 2176 1176 616 360 272 200 72 0 0 0 0 0 66 176 242 330 517 792
12 10332 6685 4032 2394 1428 805 392 140 84 21 84 0 0 0 84 36 84 120 252 420 8981 4263 2023 959 455 217 105 49 21 7 7
7 0 12 12 12 36 84 180 372 10612 6909 4158 2324 1204 609 350 266 196 70 0 0 0 0 0 60 156 216 300 444
13 18804 12150 7242 4158 2400 1410 786 378 132 78 18 78 0 0 0 78 39 78 104 182 16218 7698 3654 1734 822 390 186 90 42 18 6
6 6 0 13 13 13 39 91 195 19020 12402 7542 4350 2352 1182 582 330 252 186 66 0 0 0 0 0 52 130 182 260
14 33250 21540 12870 7295 4050 2290 1330 735 350 120 70 15 70 0 0 0 70 42 70 84 28475 13515 6415 3045 1445 685 325 155 75 35 15
5 5 5 0 14 14 14 42 98 33160 21570 13090 7635 4280 2260 1110 535 300 230 170 60 0 0 0 0 0 42 98 140
15 56156 36468 21928 12492 6844 3708 2064 1188 652 308 104 60 12 60 0 0 0 60 45 60 47996 22780 10812 5132 2436 1156 548 260 124 60 28
12 4 4 4 0 15 15 15 45 55780 36196 21832 12676 7188 3948 2048 988 468 260 200 148 52 0 0 0 0 0 30 60
16 88608 57585 34752 19968 11016 5889 3132 1722 984 537 252 84 48 9 48 0 0 0 48 48 75843 35997 17085 8109 3849 1827 867 411 195 93 45
21 9 3 3 3 0 16 16 16 88272 57237 34398 19806 11160 6201 3354 1716 816 381 210 162 120 42 0 0 0 0 0 16
17 124224 80694 48702 28102 15660 8442 4430 2322 1264 718 390 182 60 34 6 34 0 0 0 34 106530 50562 23998 11390 5406 2566 1218 578 274 130 62
30 14 6 2 2 2 0 17 17 124224 80586 48426 27766 15492 8542 4674 2498 1264 594 274 150 116 86 30 0 0 0 0 0
18 130762 84886 51158 29507 16518 9004 4770 2467 1278 690 390 211 98 32 18 3 18 0 0 0 112225 53265 25281 11999 5695 2703 1283 609 289 137 65
31 15 7 3 1 1 1 0 18 130968 85016 51162 29347 16300 8890 4822 2607 1380 692 322 147 80 62 46 16 0 0 0 0
19 856702 556204 335092 192824 107472 58466 31240 16524 8722 4600 2392 1196 564 262 140 104 70 36 0 0 734628 348674 165490 78546 37280 17694 8398 3986 1892 898 426
202 96 46 22 10 4 2 2 0 856590 555980 334698 192434 107352 58670 31558 16698 8666 4424 2262 1190 644 338 162 70 22 4 2 19
20 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 0
40 19 2 4 22 70 162 338 644 1190 2262 4424 8666 16698 31558 58670 107352 192434 334698 555980 856590 0 2 2 4 10 22 46 96 202 426 898
1892 3986 8398 17694 37280 78546 165490 348674 734628 0 0 36 70 104 140 262 564 1196 2392 4600 8722 16524 31240 58466 107472 192824 335092 556204 856702
41 0 0 0 0 16 46 62 80 147 322 692 1380 2607 4822 8890 16300 29347 51162 85016 130968 18 0 1 1 1 3 7 15 31 65 137
289 609 1283 2703 5695 11999 25281 53265 112225 0 0 0 18 3 18 32 98 211 390 690 1278 2467 4770 9004 16518 29507 51158 84886 130762
42 0 0 0 0 0 30 86 116 150 274 594 1264 2498 4674 8542 15492 27766 48426 80586 124224 17 17 0 2 2 2 6 14 30 62 130
274 578 1218 2566 5406 11390 23998 50562 106530 34 0 0 0 34 6 34 60 182 390 718 1264 2322 4430 8442 15660 28102 48702 80694 124224
43 16 0 0 0 0 0 42 120 162 210 381 816 1716 3354 6201 11160 19806 34398 57237 88272 16 16 16 0 3 3 3 9 21 45 93
195 411 867 1827 3849 8109 17085 35997 75843 48 48 0 0 0 48 9 48 84 252 537 984 1722 3132 5889 11016 19968 34752 57585 88608
44 60 30 0 0 0 0 0 52 148 200 260 468 988 2048 3948 7188 12676 21832 36196 55780 45 15 15 15 0 4 4 4 12 28 60
124 260 548 1156 2436 5132 10812 22780 47996 60 45 60 0 0 0 60 12 60 104 308 652 1188 2064 3708 6844 12492 21928 36468 56156
45 140 98 42 0 0 0 0 0 60 170 230 300 535 1110 2260 4280 7635 13090 21570 33160 98 42 14 14 14 0 5 5 5 15 35
75 155 325 685 1445 3045 6415 13515 28475 84 70 42 70 0 0 0 70 15 70 120 350 735 1330 2290 4050 7295 12870 21540 33250
46 260 182 130 52 0 0 0 0 0 66 186 252 330 582 1182 2352 4350 7542 12402 19020 195 91 39 13 13 13 0 6 6 6 18
42 90 186 390 822 1734 3654 7698 16218 182 104 78 39 78 0 0 0 78 18 78 132 378 786 1410 2400 4158 7242 12150 18804
47 444 300 216 156 60 0 0 0 0 0 70 196 266 350 609 1204 2324 4158 6909 10612 372 180 84 36 12 12 12 0 7 7 7
21 49 105 217 455 959 2023 4263 8981 420 252 120 84 36 84 0 0 0 84 21 84 140 392 805 1428 2394 4032 6685 10332
48 792 517 330 242 176 66 0 0 0 0 0 72 200 272 360 616 1176 2176 3704 5736 715 341 165 77 33 11 11 11 0 8 8
8 24 56 120 248 520 1096 2312 4872 880 561 308 132 88 33 88 0 0 0 88 24 88 144 392 792 1384 2272 3672 5624
49 1520 970 570 350 260 190 70 0 0 0 0 0 72 198 270 360 603 1098 1908 2988 1370 650 310 150 70 30 10 10 10 0 9
9 9 27 63 135 279 585 1233 2601 1680 1110 670 350 140 90 30 90 0 0 0 90 27 90 144 378 747 1278 2034 3078
50 2988 1908 1098 603 360 270 198 72 0 0 0 0 0 70 190 260 350 570 970 1520 2601 1233 585 279 135 63 27 9 9 9 0
10 10 10 30 70 150 310 650 1370 3078 2034 1278 747 378 144 90 27 90 0 0 0 90 30 90 140 350 670 1110 1680
51 5736 3704 2176 1176 616 360 272 200 72 0 0 0 0 0 66 176 242 330 517 792 4872 2312 1096 520 248 120 56 24 8 8 8
0 11 11 11 33 77 165 341 715 5624 3672 2272 1384 792 392 144 88 24 88 0 0 0 88 33 88 132 308 561 880
52 10612 6909 4158 2324 1204 609 350 266 196 70 0 0 0 0 0 60 156 216 300 444 8981 4263 2023 959 455 217 105 49 21 7 7
7 0 12 12 12 36 84 180 372 10332 6685 4032 2394 1428 805 392 140 84 21 84 0 0 0 84 36 84 120 252 420
53 19020 12402 7542 4350 2352 1182 582 330 252 186 66 0 0 0 0 0 52 130 182 260 16218 7698 3654 1734 822 390 186 90 42 18 6
6 6 0 13 13 13 39 91 195 18804 12150 7242 4158 2400 1410 786 378 132 78 18 78 0 0 0 78 39 78 104 182
54 33160 21570 13090 7635 4280 2260 1110 535 300 230 170 60 0 0 0 0 0 42 98 140 28475 13515 6415 3045 1445 685 325 155 75 35 15
5 5 5 0 14 14 14 42 98 33250 21540 12870 7295 4050 2290 1330 735 350 120 70 15 70 0 0 0 70 42 70 84
55 55780 36196 21832 12676 7188 3948 2048 988 468 260 200 148 52 0 0 0 0 0 30 60 47996 22780 10812 5132 2436 1156 548 260 124 60 28
12 4 4 4 0 15 15 15 45 56156 36468 21928 12492 6844 3708 2064 1188 652 308 104 60 12 60 0 0 0 60 45 60
56 88272 57237 34398 19806 11160 6201 3354 1716 816 381 210 162 120 42 0 0 0 0 0 16 75843 35997 17085 8109 3849 1827 867 411 195 93 45
21 9 3 3 3 0 16 16 16 88608 57585 34752 19968 11016 5889 3132 1722 984 537 252 84 48 9 48 0 0 0 48 48
57 124224 80586 48426 27766 15492 8542 4674 2498 1264 594 274 150 116 86 30 0 0 0 0 0 106530 50562 23998 11390 5406 2566 1218 578 274 130 62
30 14 6 2 2 2 0 17 17 124224 80694 48702 28102 15660 8442 4430 2322 1264 718 390 182 60 34 6 34 0 0 0 34
58 130968 85016 51162 29347 16300 8890 4822 2607 1380 692 322 147 80 62 46 16 0 0 0 0 112225 53265 25281 11999 5695 2703 1283 609 289 137 65
31 15 7 3 1 1 1 0 18 130762 84886 51158 29507 16518 9004 4770 2467 1278 690 390 211 98 32 18 3 18 0 0 0
59 856590 555980 334698 192434 107352 58670 31558 16698 8666 4424 2262 1190 644 338 162 70 22 4 2 19 734628 348674 165490 78546 37280 17694 8398 3986 1892 898 426
202 96 46 22 10 4 2 2 0 856702 556204 335092 192824 107472 58466 31240 16524 8722 4600 2392 1196 564 262 140 104 70 36 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*10 + 1*19 + 2*22 + 1*36 + 1*46 + 2*70 + 1*96 + 1*104 + 1*140 + 1*162 + 1*202 + 1*262 + 1*338 + 1*426 + 1*564 + 1*644 + 1*898 + 1*1190 + 1*1196 + 1*1892 + 1*2262 + 1*2392 +
1*4424 + 1*4600 + 1*3986 + 1*8398 + 1*8666 + 1*8722 + 1*16524 + 1*16698 + 1*17694 + 1*31240 + 1*31558 + 1*37280 + 1*58466 + 1*58670 + 1*78546 + 1*107352 + 1*107472 + 1*165490 + 1*192434 +
1*192824 + 1*334698 + 1*335092 + 1*348674 + 1*555980 + 1*556204 + 1*734628 + 1*856590 + 1*856702) +
4(8*0 + 3*1 + 2*3 + 1*7 + 1*15 + 1*16 + 3*18 + 1*31 + 1*32 + 1*46 + 1*62 + 1*65 + 1*80 + 1*98 + 1*137 + 1*147 + 1*211 + 1*289 + 1*322 + 1*390 + 1*609 + 1*690 + 1*692 + 1*1278 + 1*1283 + 1*1380 +
1*2467 + 1*2607 + 1*2703 + 1*4770 + 1*4822 + 1*5695 + 1*8890 + 1*9004 + 1*11999 + 1*16300 + 1*16518 + 1*25281 + 1*29347 + 1*29507 + 1*51158 + 1*51162 + 1*53265 + 1*84886 + 1*85016 + 1*112225 +
1*130762 + 1*130968) +
4(9*0 + 3*2 + 2*6 + 1*14 + 2*17 + 2*30 + 3*34 + 1*60 + 1*62 + 1*86 + 1*116 + 1*130 + 1*150 + 1*182 + 2*274 + 1*390 + 1*578 + 1*594 + 1*718 + 1*1218 + 2*1264 + 1*2322 + 1*2498 + 1*2566 + 1*4430 +
1*4674 + 1*5406 + 1*8442 + 1*8542 + 1*11390 + 1*15492 + 1*15660 + 1*23998 + 1*27766 + 1*28102 + 1*48426 + 1*48702 + 1*50562 + 1*80586 + 1*80694 + 1*106530 + 1*124224 + 1*124224) +
4(9*0 + 3*3 + 2*9 + 4*16 + 1*21 + 1*42 + 1*45 + 4*48 + 1*84 + 1*93 + 1*120 + 1*162 + 1*195 + 1*210 + 1*252 + 1*381 + 1*411 + 1*537 + 1*816 + 1*867 + 1*984 + 1*1716 + 1*1722 + 1*1827 + 1*3132 +
1*3354 + 1*3849 + 1*5889 + 1*6201 + 1*8109 + 1*11016 + 1*11160 + 1*17085 + 1*19806 + 1*19968 + 1*34398 + 1*34752 + 1*35997 + 1*57237 + 1*57585 + 1*75843 + 1*88272 + 1*88608) +
4(9*0 + 3*4 + 2*12 + 3*15 + 1*28 + 1*30 + 2*45 + 1*52 + 6*60 + 1*104 + 1*124 + 1*148 + 1*200 + 2*260 + 1*308 + 1*468 + 1*548 + 1*652 + 1*988 + 1*1156 + 1*1188 + 1*2048 + 1*2064 + 1*2436 +
1*3708 + 1*3948 + 1*5132 + 1*6844 + 1*7188 + 1*10812 + 1*12492 + 1*12676 + 1*21832 + 1*21928 + 1*22780 + 1*36196 + 1*36468 + 1*47996 + 1*55780 + 1*56156) +
4(9*0 + 3*5 + 3*14 + 2*15 + 1*35 + 3*42 + 1*60 + 4*70 + 1*75 + 1*84 + 2*98 + 1*120 + 1*140 + 1*155 + 1*170 + 1*230 + 1*300 + 1*325 + 1*350 + 1*535 + 1*685 + 1*735 + 1*1110 + 1*1330 + 1*1445 +
1*2260 + 1*2290 + 1*3045 + 1*4050 + 1*4280 + 1*6415 + 1*7295 + 1*7635 + 1*12870 + 1*13090 + 1*13515 + 1*21540 + 1*21570 + 1*28475 + 1*33160 + 1*33250) +
4(9*0 + 3*6 + 3*13 + 2*18 + 2*39 + 1*42 + 1*52 + 1*66 + 4*78 + 1*90 + 1*91 + 1*104 + 1*130 + 1*132 + 2*182 + 2*186 + 1*195 + 1*252 + 1*260 + 1*330 + 1*378 + 1*390 + 1*582 + 1*786 + 1*822 +
1*1182 + 1*1410 + 1*1734 + 1*2352 + 1*2400 + 1*3654 + 1*4158 + 1*4350 + 1*7242 + 1*7542 + 1*7698 + 1*12150 + 1*12402 + 1*16218 + 1*18804 + 1*19020) +
4(9*0 + 3*7 + 3*12 + 2*21 + 2*36 + 1*49 + 1*60 + 1*70 + 5*84 + 1*105 + 1*120 + 1*140 + 1*156 + 1*180 + 1*196 + 1*216 + 1*217 + 1*252 + 1*266 + 1*300 + 1*350 + 1*372 + 1*392 + 1*420 + 1*444 +
1*455 + 1*609 + 1*805 + 1*959 + 1*1204 + 1*1428 + 1*2023 + 1*2324 + 1*2394 + 1*4032 + 1*4158 + 1*4263 + 1*6685 + 1*6909 + 1*8981 + 1*10332 + 1*10612) +
4(9*0 + 3*8 + 3*11 + 2*24 + 2*33 + 1*56 + 1*66 + 1*72 + 1*77 + 4*88 + 1*120 + 1*132 + 1*144 + 1*165 + 1*176 + 1*200 + 1*242 + 1*248 + 1*272 + 1*308 + 1*330 + 1*341 + 1*360 + 1*392 + 1*517 +
1*520 + 1*561 + 1*616 + 1*715 + 2*792 + 1*880 + 1*1096 + 1*1176 + 1*1384 + 1*2176 + 1*2272 + 1*2312 + 1*3672 + 1*3704 + 1*4872 + 1*5624 + 1*5736) +
4(9*0 + 3*9 + 3*10 + 2*27 + 2*30 + 1*63 + 2*70 + 1*72 + 4*90 + 1*135 + 1*140 + 1*144 + 1*150 + 1*190 + 1*198 + 1*260 + 1*270 + 1*279 + 1*310 + 2*350 + 1*360 + 1*378 + 1*570 + 1*585 + 1*603 +
1*650 + 1*670 + 1*747 + 1*970 + 1*1098 + 1*1110 + 1*1233 + 1*1278 + 1*1370 + 1*1520 + 1*1680 + 1*1908 + 1*2034 + 1*2601 + 1*2988 + 1*3078) +
2(58*0 + 2*18) +
18(60*0)
= 22970756 + 3509180 + 3331296 + 2372116 + 1502116 + 893252 + 512948 + 292276 + 174564 + 124052 + 72
= 35682628
Value repetition frequencies = 4(51*1 + 3*2 + 1*3) +
4(44*1 + 1*2 + 2*3 + 1*8) +
4(35*1 + 5*2 + 2*3 + 1*9) +
4(38*1 + 1*2 + 1*3 + 2*4 + 1*9) +
4(33*1 + 3*2 + 2*3 + 1*6 + 1*9) +
4(34*1 + 2*2 + 3*3 + 1*4 + 1*9) +
4(33*1 + 4*2 + 2*3 + 1*4 + 1*9) +
4(36*1 + 2*2 + 2*3 + 1*5 + 1*9) +
4(35*1 + 3*2 + 2*3 + 1*4 + 1*9) +
4(33*1 + 4*2 + 2*3 + 1*4 + 1*9) +
2(1*2 + 1*58) +
18(1*60)
= 3600
Number of distinct row element sets = 12
Number of rows = 1*2 + 10*4 + 1*18
= 60
Number of distinct values = 355
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Frequency 1528 12 24 20 20 12 20 16 12 20 16 12 20 12 16 24 20 8 24 4
Distinct values 21 22 24 27 28 30 31 32 33 34 35 36 39 42 45 46 48 49 52 56
Frequency 12 8 8 8 4 20 4 4 8 12 4 12 8 20 12 8 16 4 8 4
Distinct values 60 62 63 65 66 70 72 75 77 78 80 84 86 88 90 91 93 96 98 104
Frequency 36 8 4 4 8 36 8 4 4 16 4 28 4 16 20 4 4 4 12 12
Distinct values 105 116 120 124 130 132 135 137 140 144 147 148 150 155 156 162 165 170 176 180
Frequency 4 4 16 4 8 8 4 4 16 8 4 4 8 4 4 8 4 4 4 4
Distinct values 182 186 190 195 196 198 200 202 210 211 216 217 230 242 248 252 260 262 266 270
Frequency 12 8 4 8 4 4 8 4 4 4 4 4 4 4 4 12 16 4 4 4
Distinct values 272 274 279 289 300 308 310 322 325 330 338 341 350 360 372 378 381 390 392 411
Frequency 4 8 4 4 8 8 4 4 4 8 4 4 16 8 4 8 4 12 8 4
Distinct values 420 426 444 455 468 517 520 535 537 548 561 564 570 578 582 585 594 603 609 616
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 4
Distinct values 644 650 652 670 685 690 692 715 718 735 747 786 792 805 816 822 867 880 898 959
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4
Distinct values 970 984 988 1096 1098 1110 1156 1176 1182 1188 1190 1196 1204 1218 1233 1264 1278 1283 1330 1370
Frequency 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 8 8 4 4 4
Distinct values 1380 1384 1410 1428 1445 1520 1680 1716 1722 1734 1827 1892 1908 2023 2034 2048 2064 2176 2260 2262
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 2272 2290 2312 2322 2324 2352 2392 2394 2400 2436 2467 2498 2566 2601 2607 2703 2988 3045 3078 3132
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 3354 3654 3672 3704 3708 3849 3948 3986 4032 4050 4158 4263 4280 4350 4424 4430 4600 4674 4770 4822
Frequency 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4
Distinct values 4872 5132 5406 5624 5695 5736 5889 6201 6415 6685 6844 6909 7188 7242 7295 7542 7635 7698 8109 8398
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 8442 8542 8666 8722 8890 8981 9004 10332 10612 10812 11016 11160 11390 11999 12150 12402 12492 12676 12870 13090
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 13515 15492 15660 16218 16300 16518 16524 16698 17085 17694 18804 19020 19806 19968 21540 21570 21832 21928 22780 23998
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 25281 27766 28102 28475 29347 29507 31240 31558 33160 33250 34398 34752 35997 36196 36468 37280 47996 48426 48702 50562
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 51158 51162 53265 55780 56156 57237 57585 58466 58670 75843 78546 80586 80694 84886 85016 88272 88608 106530 107352 107472
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 112225 124224 130762 130968 165490 192434 192824 334698 335092 348674 555980 556204 734628 856590 856702
Frequency 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 282*4 + 33*8 + 14*12 + 10*16 + 9*20 + 3*24 + 1*28 + 2*36 + 1*1528
= 3600
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 32*51 + 4*52 + 4*57
= 2072
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1468
Number of possible SN-EN pairs with SN != EN = 59*60
= 3540
