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 A331509 Array read by antidiagonals: A(n,k) is the number of nonisomorphic T_0 n-regular set-systems on a k-set. 5
 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 3, 0, 0, 1, 0, 1, 6, 3, 0, 0, 1, 0, 1, 15, 19, 1, 0, 0, 1, 0, 1, 42, 141, 29, 0, 0, 0, 1, 0, 1, 109, 1571, 769, 23, 0, 0, 0, 1, 0, 1, 320 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,18 COMMENTS An n-regular set-system is a finite set of nonempty sets in which each element appears in n blocks. A set-system is T_0 if for every two distinct elements there exists a block containing one but not the other element. A(n,k) is the number of nonequivalent binary matrices with k distinct columns and any number of distinct nonzero rows with n ones in every column up to permutation of rows and columns. LINKS EXAMPLE Array begins: ================================= n\k | 0 1 2 3  4   5    6   7 ----+----------------------------   0 | 1 1 0 0  0   0    0   0 ...   1 | 1 1 1 1  1   1    1   1 ...   2 | 1 0 1 3  6  15   42 109 ...   3 | 1 0 0 3 19 141 1571 ...   4 | 1 0 0 1 29 769 ...   5 | 1 0 0 0 23 ...   ... The A(2,3) = 3 matrices are:   [1 1 1]    [1 1 0]    [1 1 0]   [1 0 0]    [1 0 1]    [1 0 1]   [0 1 0]    [0 1 0]    [0 1 1]   [0 0 1]    [0 0 1] CROSSREFS Row 2 appears to be A005368. Cf. A330942, A331039, A331461, A331508, A331510. Sequence in context: A324874 A324862 A324864 * A171913 A074936 A035655 Adjacent sequences:  A331506 A331507 A331508 * A331510 A331511 A331512 KEYWORD nonn,tabl,more AUTHOR Andrew Howroyd, Jan 18 2020 STATUS approved

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Last modified November 24 07:53 EST 2020. Contains 338607 sequences. (Running on oeis4.)