A331509 Array read by antidiagonals: A(n,k) is the number of nonisomorphic T_0 n-regular set-systems on a k-set.

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

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. Row 3 is A331716.

Cf. A330942, A331039, A331461, A331508, A331510.

Sequence in context: A324874 A324862 A324864 * A171913 A342154 A074936

Adjacent sequences: A331506 A331507 A331508 * A331510 A331511 A331512

Keyword

nonn,tabl,more

Author

Andrew Howroyd, Jan 18 2020

Status

approved