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

Offset: 1

Author

Andrew Howroyd, Jan 13 2020

Keywords

• nonn

Comments

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

Examples

			The a(4) = 7 matrices are:
  [1 0 0 0]  [1 1]  [2 1]  [2 0]  [1 2]  [3]  [4]
  [0 1 0 0]  [1 0]  [0 1]  [0 2]  [1 0]  [1]
  [0 0 1 0]  [0 1]
  [0 0 0 1]
		

Crossrefs

Cf. A000009, A330158, A331160.

Formula

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

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