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%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
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