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

1,2

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:
  [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.

Sequence in context: A086885 A324598 A229794 * A376068 A082734 A332526

Adjacent sequences: A331315 A331316 A331317 * A331319 A331320 A331321

Keyword

nonn

Author

Andrew Howroyd, Jan 13 2020

Status

approved