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

Author

Andrew Howroyd, Jan 24 2020

Keywords

• nonn

Comments

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

Examples

			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.

Formula

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