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

Offset: 0

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(2) = 7 matrices are:
   [2 1]   [2 0]   [1 2]   [1 1]   [2 0]   [1 0]   [1 0]
   [0 1]   [0 2]   [1 0]   [1 0]   [0 1]   [1 0]   [1 0]
                           [0 1]   [0 1]   [0 2]   [0 1]
                                                   [0 1]
See the example in A331197 for the a(3) = 28 case.
		

Links

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

Crossrefs

Column k=2 of A331161.

Cf. A000041, A002774, A331197.

Formula

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