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

1,2

Comments

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

Links

Table of n, a(n) for n=1..32.

Formula

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

a(p) = 2 for prime p.

Example

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.

Sequence in context: A126984 A159749 A227293 * A359442 A102416 A333595

Adjacent sequences: A331388 A331389 A331390 * A331392 A331393 A331394

Keyword

nonn

Author

Andrew Howroyd, Jan 15 2020

Status

approved