A331706 Number of nonnegative integer matrices with 2 distinct columns and any number of distinct nonzero rows with column sums n and columns in decreasing lexicographic order.

0, 1, 6, 42, 268, 1239, 7278, 40828, 201084, 1044693, 5171998, 24532674, 116470596, 546141979, 2505755010, 11318525016, 50046272884, 219637249269, 944072863998, 4029243437158, 16977344149608, 70370874102975, 289702060529770, 1177283903977008, 4740700176809748

Offset: 0

Author

Andrew Howroyd, Jan 25 2020

Keywords

• nonn

Comments

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

Examples

			The a(2) = 6 matrices are:
   [1 1]  [1 0]  [1 0]  [2 1]  [2 0]  [1 0]
   [1 0]  [1 1]  [0 1]  [0 1]  [0 2]  [1 2]
   [0 1]  [0 1]  [1 1]
		

Crossrefs

Column k=2 of A331570.

Cf. A032020, A331646, A331707.

Formula

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