A331318 - OEIS

A331318

Number of nonnegative integer matrices with total sum n, distinct columns with equal sums and any number of distinct nonzero rows in decreasing lexicographic order.

1, 2, 3, 7, 4, 47, 6, 317, 326, 3730, 13, 78625, 19, 1372944, 824798, 36641157, 39, 1211620030, 55, 41615035330, 9881046310, 1743624029061, 105, 85034153219895, 10679934643, 4476101995508420, 385900622506127, 268621480352669227, 257, 17969848317035340096

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OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

a(n) = Sum_{d|n} A331160(n/d, d).

a(p) = A000009(n) + 1 for prime p.

EXAMPLE

The a(4) = 7 matrices are: