A098805 Array read by antidiagonals: Numerical sequences of Fibonacci-like polynomials produced by m-ary Huffman trees of maximum height for absolutely ordered sequences.

1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 5, 4, 2, 1, 1, 8, 8, 5, 2, 1, 1, 13, 16, 11, 6, 2, 1, 1, 21, 32, 26, 14, 7, 2, 1, 1, 34, 64, 59, 38, 17, 8, 2, 1, 1, 55, 128, 137, 94, 52, 20, 9, 2, 1, 1, 89, 256, 314, 246, 137, 68, 23, 10, 2, 1, 1, 144, 512, 725, 622, 397, 188, 86, 26, 11, 2, 1, 1, 233, 1024

Offset

0,4

Links

Table of n, a(n) for n=0..79.

Alex Vinokur, Fibonacci connection between Huffman codes and Wythoff array, E-print, 2004, 10 pages.

Formula

T[0, m] = 1, T[1, m] = 1, T[2, m] = 2; T[n, m] = T[n-1, m] + m*T[n-2, m] when n > 2; m > 0.

Example

Top left corner of array:
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946
1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288
1 1 2 5 11 26 59 137 314 725 1667 3842 8843 20369 46898 108005 248699 572714 1318811 3036953 6993386
1 1 2 6 14 38 94 246 622 1606 4094 10518 26894 68966 176542 452406 1158574 2968198 7602494 19475286 49885262
1 1 2 7 17 52 137 397 1082 3067 8477 23812 66197 185257 516242 1442527 4023737 11236372 31355057 87536917 244312202
1 1 2 8 20 68 188 596 1724 5300 15644 47444 141308 425972 1273820 3829652 11472572 34450484 103285916 309988820 929704316
1 1 2 9 23 86 247 849 2578 8521 26567 86214 272183 875681 2780962 8910729 28377463 90752566 289394807 924662769 2950426418
1 1 2 10 26 106 314 1162 3674 12970 42362 146122 485018 1653994 5534138 18766090 63039194 213167914 717481466 2422824778 8162676506
1 1 2 11 29 128 389 1541 5042 18911 64289 234488 813089 2923481 10241282 36552611 128724149 457697648 1616214989 5735493821 20281428722
1 1 2 12 32 152 472 1992 6712 26632 93752 360072 1297592 4898312 17874232 66857352 245599672 914173192 3370169912 12511901832 46213600952
1 1 2 13 35 178 563 2521 8714 36445 132299 533194 1988483 7853617 29726930 116116717 443112947 1720396834 6594639251 25519004425 98060036186
1 1 2 14 38 206 662 3134 11078 48686 181622 765854 2945318 12135566 47479382 193106174 762858758 3080132846 12234437942 49196032094 196009287398
1 1 2 15 41 236 769 3837 13834 63715 243557 1071852 4238093 18172169 73267378 309505575 1261981489 5285553964 21691313321 90403514853 372390588026
1 1 2 16 44 268 884 4636 17012 81916 320084 1466908 5948084 26484796 109757972 480545116 2017156724 8744788348 36984982484 159412019356 677201774132
1 1 2 17 47 302 1007 5537 20642 103697 413327 1968782 8168687 37700417 160230722 725736977 3129197807 14015252462 60953219567 271182006497 1185480300002
1 1 2 18 50 338 1138 6546 24754 129490 525554 2597394 11006258 52564562 228664690 1069697682 4728332722 21843495634 97496819186 446992749330 2006941856306
1 1 2 19 53 376 1277 7669 29378 159751 659177 3374944 14580953 71955001 319831202 1543066219 6980196653 33212322376 151875665477 716485145869 3298371458978
1 1 2 20 56 416 1424 8912 34544 194960 816752 4326032 19027568 96896144 439392368 2183522960 10092585584 49395998864 231062539376 1120190518928 5279316227696
1 1 2 21 59 458 1579 10281 40282 235621 1000979 5477778 24496379 128574161 594005362 3036914421 14323016299 72024390298 344161699979 1712625115641 8251697415242
1 1 2 22 62 502 1742 11782 46622 282262 1214702 6859942 31153982 168352822 791432462 4158488902 19987138142 103156916182 502899679022 2566038002662 12624031583102
1 1 2 23 65 548 1913 13421 53594 335435 1460909 8505044 39184133 217790057 1040656850 5614248047 27468041897 145367250884 722196130721 3774908399285 18941027144426

Crossrefs

Sequence in context: A180360 A318805 A175331 * A168396 A049286 A308477

Adjacent sequences: A098802 A098803 A098804 * A098806 A098807 A098808

Keyword

easy,nonn,tabl

Author

Alex Vinokur (alexvn(AT)barak-online.net), Nov 02 2004

Status

approved