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A363845
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Triangle read by rows: T(n,k) = number of connected n-node graphs with k nodes in distinguished bipartite block, k = 0..n.
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3
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1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 4, 4, 1, 0, 0, 1, 6, 13, 6, 1, 0, 0, 1, 9, 34, 34, 9, 1, 0, 0, 1, 12, 76, 150, 76, 12, 1, 0, 0, 1, 16, 155, 558, 558, 155, 16, 1, 0, 0, 1, 20, 290, 1824, 3529, 1824, 290, 20, 1, 0, 0, 1, 25, 510, 5375, 19687, 19687, 5375, 510, 25, 1, 0, 0, 1, 30, 853, 14549, 98726, 194203, 98726, 14549, 853, 30, 1, 0
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OFFSET
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0,13
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COMMENTS
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Also, rectangular array read by antidiagonals: A(m,n) = number of distinct m X n binary matrices M up to permutations of rows or columns such that M represents the reduced adjacency matrix of a connected bipartite graph.
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LINKS
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EXAMPLE
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n=0: 1,
n=1: 1, 1,
n=2: 0, 1, 0,
n=3: 0, 1, 1, 0,
n=4: 0, 1, 2, 1, 0,
n=5: 0, 1, 4, 4, 1, 0,
n=6: 0, 1, 6, 13, 6, 1, 0,
n=7: 0, 1, 9, 34, 34, 9, 1, 0,
n=8: 0, 1, 12, 76, 150, 76, 12, 1, 0,
n=9: 0, 1, 16, 155, 558, 558, 155, 16, 1, 0,
...
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CROSSREFS
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Inverse bivariate Euler transform of A028657.
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KEYWORD
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AUTHOR
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STATUS
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approved
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