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A123551
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Triangle read by rows: T(n,k) gives number of unlabeled graphs without endpoints on n nodes and k edges, (n >= 0, 0 <= k <= n(n-1)/2).
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2
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1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 2, 4, 3, 2, 1, 1, 1, 0, 0, 1, 1, 2, 6, 8, 13, 16, 13, 8, 5, 2, 1, 1, 1, 0, 0, 1, 1, 2, 6, 10, 22, 48, 76, 97, 102, 84, 60, 39, 20, 10, 5, 2, 1, 1, 1, 0, 0, 1, 1, 2, 6, 10, 25, 64, 152, 331, 617, 930, 1173, 1253, 1140
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OFFSET
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0,21
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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, 1977.
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LINKS
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R. W. Robinson, Rows 0 through 16, flattened
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FORMULA
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T(n,k) = A008406(n,k) - A240168(n,k). - Andrew Howroyd, Apr 16 2021
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EXAMPLE
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Triangle begins:
n = 0
k = 0 : 1
******************** total (n = 0) = 1
n = 1
k = 0 : 1
******************** total (n = 1) = 1
n = 2
k = 0 : 1
k = 1 : 0
******************** total (n = 2) = 1
n = 3
k = 0 : 1
k = 1 : 0
k = 2 : 0
k = 3 : 1
******************** total (n = 3) = 2
n = 4
k = 0 : 1
k = 1 : 0
k = 2 : 0
k = 3 : 1
k = 4 : 1
k = 5 : 1
k = 6 : 1
******************** total (n = 4) = 5
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CROSSREFS
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Row sums are A004110.
Cf. A008406, A240168.
Sequence in context: A307500 A049245 A123547 * A286275 A029717 A135567
Adjacent sequences: A123548 A123549 A123550 * A123552 A123553 A123554
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane, Nov 14 2006
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STATUS
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approved
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