A331510 Array read by antidiagonals: A(n,k) is the number of nonequivalent binary matrices with k columns and any number of distinct nonzero rows with n ones in every column up to permutation of rows and columns.

1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 3, 1, 0, 1, 1, 5, 4, 0, 0, 1, 1, 7, 12, 3, 0, 0, 1, 1, 11, 36, 23, 1, 0, 0, 1, 1, 15, 124, 191, 30, 0, 0, 0, 1, 1, 22, 412, 2203, 837, 23, 0, 0, 0, 1, 1, 30, 1500, 31313, 41664, 2688, 12, 0, 0, 0, 1

Offset: 0

Author

Andrew Howroyd, Jan 18 2020

Keywords

• nonn
• tabl
• more

Examples

			Array begins:
=================================
n\k | 0 1 2 3  4   5    6   7
----+----------------------------
  0 | 1 1 1 1  1   1    1   1 ...
  1 | 1 1 2 3  5   7   11  15 ...
  2 | 1 0 1 4 12  36  124 412 ...
  3 | 1 0 0 3 23 191 2203 ...
  4 | 1 0 0 1 30 837 ...
  5 | 1 0 0 0 23 ...
  ...
The A(2,3) = 4 matrices are:
  [1 1 1]  [1 1 0]  [1 1 1]  [1 1 0]
  [1 0 0]  [1 0 1]  [1 1 0]  [1 0 1]
  [0 1 0]  [0 1 0]  [0 0 1]  [0 1 1]
  [0 0 1]  [0 0 1]
		

Crossrefs

Rows n=1..3 are A000041, A331717, A331718.

Column k=5 is A331719.

Cf. A188445, A330942, A331461, A331508, A331509.

Formula

A(n,k) = 0 for k > 0, n > 2^(k-1).

A(n,k) = A(2^(k-1) - n, k) for k > 0, n <= 2^(k-1).

Extensions

a(58)-a(65) from Andrew Howroyd, Feb 08 2020