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

0,3

Comments

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

Links

Table of n, a(n) for n=0..24.

Formula

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

Example

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.

Sequence in context: A283328 A377194 A343363 * A074429 A062310 A377198

Adjacent sequences: A331703 A331704 A331705 * A331707 A331708 A331709

Keyword

nonn

Author

Andrew Howroyd, Jan 25 2020

Status

approved