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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

Table of n, a(n) for n=0..57.

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.)