A331651 Number of binary matrices with distinct nonzero rows, a total of n ones and distinct columns each with the same number of ones and columns in decreasing lexicographic order.

1, 1, 1, 4, 1, 18, 1, 231, 185, 3265, 1, 78115, 1, 1287063, 2711905, 32669406, 1, 1568741156, 1, 29488026590, 232383728379, 967596779632, 1, 147586156446663, 585810653617, 1509052435744561, 61466235823794522, 96920622619890141, 1, 47758782949643628393

Offset

1,4

Comments

The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = Sum_{d|n} A331569(n/d, d).

Example

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

Crossrefs

Cf. A331569.

Sequence in context: A171589 A126331 A013631 * A113355 A201201 A077102

Adjacent sequences: A331648 A331649 A331650 * A331652 A331653 A331654

Keyword

nonn

Author

Andrew Howroyd, Jan 24 2020

Status

approved