A331711 Number of nonnegative integer matrices with 2 columns and any number of distinct nonzero rows with column sums n and columns in nonincreasing lexicographic order.

1, 2, 7, 45, 271, 1244, 7289, 40841, 201103, 1044720, 5172055, 24532739, 116470697, 546142112, 2505755203, 11318525367, 50046273319, 219637249886, 944072864849, 4029243438335, 16977344151163, 70370874105726, 289702060533067, 1177283903981765, 4740700176816041

Offset: 0

Author

Andrew Howroyd, Jan 25 2020

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Column k=2 of A331572.

Cf. A032020, A331646, A331712.

Formula

a(n) = (A331646(n) + A032020(n)) / 2.