A331391 Number of binary matrices with a total of n ones, distinct columns each with the same number of ones and nonzero rows in nonincreasing lexicographic order.

1, 2, 2, 4, 2, 14, 2, 76, 31, 801, 2, 12797, 2, 233247, 28480, 5560377, 2, 160866915, 2, 5351339038, 193927186, 208746406130, 2, 9342273087807, 5289613, 470405726166256, 4946464287635, 26636935297440055, 2, 1679266767908385729, 2, 116818412262277969513

Offset: 1

Author

Andrew Howroyd, Jan 15 2020

Keywords

• nonn

Comments

The condition that the rows be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of rows.

Examples

			The a(4) = 4 matrices are:
   [1 0 0 0]   [1]   [1 0]   [1 1]
   [0 1 0 0]   [1]   [1 0]   [1 0]
   [0 0 1 0]   [1]   [0 1]   [0 1]
   [0 0 0 1]   [1]   [0 1]
		

Crossrefs

Cf. A331126.

Formula

a(n) = Sum{d|n} A331126(n/d, d).

a(p) = 2 for prime p.