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A055080
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Triangle T(n,k) read by rows, giving number of k-member minimal covers of an unlabeled n-set, k=1..n.
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15
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1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 6, 9, 4, 1, 1, 9, 23, 17, 5, 1, 1, 12, 51, 65, 28, 6, 1, 1, 16, 103, 230, 156, 43, 7, 1, 1, 20, 196, 736, 863, 336, 62, 8, 1, 1, 25, 348, 2197, 4571, 2864, 664, 86, 9, 1, 1, 30, 590, 6093, 22952, 25326, 8609, 1229, 115, 10, 1, 1, 36, 960
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OFFSET
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1,5
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COMMENTS
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Also number of unlabeled split graphs on n vertices and with a k-element clique (cf. A048194).
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 2, 1;
1, 4, 3, 1;
1, 6, 9, 4, 1;
1, 9, 23, 17, 5, 1;
1, 12, 51, 65, 28, 6, 1;
1, 16, 103, 230, 156, 43, 7, 1;
1, 20, 196, 736, 863, 336, 62, 8, 1;
...
There are four minimal covers of an unlabeled 3-set: one 1-cover {{1,2,3}}, two 2-covers {{1,2},{3}}, {{1,2},{1,3}} and one 3-cover {{1},{2},{3}}.
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PROG
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(PARI) \\ Needs A(n, m) from A028657.
T(n, k) = A(n-k, k) - if(k<n, A(n-1-k, k))
{ for(n=1, 10, for(k=1, n, print1(T(n, k), ", ")); print) } \\ Andrew Howroyd, Feb 28 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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