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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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4
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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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Table of n, a(n) for n=1..69.
R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
Vladeta Jovovic, Binary matrices up to row and column permutations
G. F. Royle, Counting Set Covers and Split Graphs, J. Integer Seqs., 3 (2000), #00.2.6.
Eric Weisstein's World of Mathematics, Minimal covers
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EXAMPLE
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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],
...;
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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CROSSREFS
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Row sums give A048194. Cf. A035348 for labeled case. Cf. A005783-A005786, A055066, A005744-A005748, A005771.
See also A002620.
Sequence in context: A034781 A110470 A347699 * A034367 A058717 A034371
Adjacent sequences: A055077 A055078 A055079 * A055081 A055082 A055083
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KEYWORD
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nonn,tabl
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AUTHOR
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Vladeta Jovovic, Jun 13 2000
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STATUS
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approved
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