A331197 - OEIS

%I #11 Jan 24 2020 15:54:39

%S 0,1,7,28,104,332,1032,2983,8384,22622,59479,151902,379616,927521,

%T 2224100,5236410,12130549,27669296,62229605,138095206,302672402,

%U 655627183,1404598865,2977830134,6251059210,12999297747,26791987616,54750232180,110977385294,223204454700,445590973235

%N 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.

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

%H Andrew Howroyd, <a href="/A331197/b331197.txt">Table of n, a(n) for n = 0..400</a>

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

%e The a(2) = 7 matrices are:

%e    [2 1]   [2 0]   [1 2]   [1 1]   [2 0]   [1 0]   [1 0]

%e    [0 1]   [0 2]   [1 0]   [1 0]   [0 1]   [1 0]   [1 0]

%e                            [0 1]   [0 1]   [0 2]   [0 1]

%e                                                    [0 1]

%e See the example in A331197 for the a(3) = 28 case.

%Y Column k=2 of A331161.

%Y Cf. A000041, A002774, A331197.

%K nonn

%O 0,3

%A _Andrew Howroyd_, Jan 11 2020