A331197 - OEIS

A331197

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

0, 1, 7, 28, 104, 332, 1032, 2983, 8384, 22622, 59479, 151902, 379616, 927521, 2224100, 5236410, 12130549, 27669296, 62229605, 138095206, 302672402, 655627183, 1404598865, 2977830134, 6251059210, 12999297747, 26791987616, 54750232180, 110977385294, 223204454700, 445590973235

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OFFSET

0,3

COMMENTS

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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..400

FORMULA

a(n) = A002774(n) - A000041(n).

EXAMPLE

The a(2) = 7 matrices are:

[2 1] [2 0] [1 2] [1 1] [2 0] [1 0] [1 0]