A331651 - OEIS

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

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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.