A330158 Number of nonnegative integer matrices with total sum n, distinct columns with equal sums and any number of nonzero rows in nonincreasing lexicographic order.

1, 3, 4, 13, 8, 83, 16, 530, 630, 5620, 57, 119889, 102, 1901749, 1498322, 50091143, 298, 1649302673, 491, 54919254373, 16723808377, 2269075359300, 1256, 110133775311277, 26852941986, 5707320920415984, 622570195638208, 339574840900645411, 4566, 22572315004012650868

Offset: 1

Author

Andrew Howroyd, Jan 11 2020

Keywords

• nonn

Comments

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

Examples

			The a(4) = 13 matrices are:
  [1 0 0 0]  [1 0]  [1]  [1 1]  [2 0]  [1 0]  [2]
  [0 1 0 0]  [1 0]  [1]  [1 0]  [0 1]  [1 0]  [1]
  [0 0 1 0]  [0 1]  [1]  [0 1]  [0 1]  [0 2]  [1]
  [0 0 0 1]  [0 1]  [1]
.
  [2 1]  [2 0]  [1 2]  [3]  [2]  [4]
  [0 1]  [0 2]  [1 0]  [1]  [2]
		

Crossrefs

Cf. A331161.

Formula

a(n) = Sum_{d|n} A331161(n/d, d).