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

0,3

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]
   [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.

Crossrefs

Column k=2 of A331161.

Cf. A000041, A002774, A331197.

Sequence in context: A219411 A224404 A370487 * A024207 A000416 A000417

Adjacent sequences: A331194 A331195 A331196 * A331198 A331199 A331200

Keyword

nonn

Author

Andrew Howroyd, Jan 11 2020

Status

approved