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A123545
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Triangle read by rows: T(n,k) = number of unlabeled connected graphs on n nodes with degree >= 3 at each node (n >= 1, 0 <= k <= n(n-1)/2).
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9
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 5, 4, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 18, 30, 34, 29, 17, 9, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 35, 136, 309, 465, 505, 438, 310, 188, 103, 52, 23
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listen;
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OFFSET
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1,35
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REFERENCES
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R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
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LINKS
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EXAMPLE
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Triangle begins:
n = 1
k = 0 : 0
************************ TOTAL (n = 1) = 0
n = 2
k = 0 : 0
k = 1 : 0
************************ TOTAL (n = 2) = 0
n = 3
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
************************ TOTAL (n = 3) = 0
n = 4
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
k = 4 : 0
k = 5 : 0
k = 6 : 1
************************ TOTAL (n = 4) = 1
n = 5
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
k = 4 : 0
k = 5 : 0
k = 6 : 0
k = 7 : 0
k = 8 : 1
k = 9 : 1
k = 10 : 1
************************ TOTAL (n = 5) = 3
Transposed table:
Nodes Sums
Edges-----------------------------------------------------|-------
6 | 1 . . . . . . . . . | 1
7 | . . . . . . . . . . | 0
8 | . 1 . . . . . . . . | 1
9 | . 1 2 . . . . . . . | 3
10 | . 1 4 . . . . . . . | 5
11 | . . 5 4 . . . . . . | 9
12 | . . 4 18 5 . . . . . | 27
13 | . . 2 30 35 . . . . . | 67
14 | . . 1 34 136 27 . . . . | 198
15 | . . 1 29 309 288 19 . . . | 646
16 | . . . 17 465 1377 357 . . . | 2216
17 | . . . 9 505 3978 3478 208 . . | 8178
18 | . . . 5 438 7956 18653 4958 85 . | 32085
19 | . . . 2 310 11904 65011 50575 4291 . | 132093
20 | . . . 1 188 14134 163812 302854 85421 1958 | 568368
(End)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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