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

0,8

Links

Table of n, a(n) for n=0..65.

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).

Example

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.

Sequence in context: A339218 A263412 A321258 * A319854 A124035 A204184

Adjacent sequences: A331507 A331508 A331509 * A331511 A331512 A331513

Keyword

nonn,tabl,more

Author

Andrew Howroyd, Jan 18 2020

Extensions

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

Status

approved