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%I #6 Jan 25 2020 20:55:43
%S 1,2,7,45,271,1244,7289,40841,201103,1044720,5172055,24532739,
%T 116470697,546142112,2505755203,11318525367,50046273319,219637249886,
%U 944072864849,4029243438335,16977344151163,70370874105726,289702060533067,1177283903981765,4740700176816041
%N Number of nonnegative integer matrices with 2 columns and any number of distinct nonzero rows with column sums n and columns in nonincreasing lexicographic order.
%C The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.
%F a(n) = (A331646(n) + A032020(n)) / 2.
%e The a(2) = 2 matrices are:
%e [1 1] [1 0] [1 0] [2 1] [2 0] [1 0] [2 2]
%e [1 0] [1 1] [0 1] [0 1] [0 2] [1 2]
%e [0 1] [0 1] [1 1]
%Y Column k=2 of A331572.
%Y Cf. A032020, A331646, A331712.
%K nonn
%O 0,2
%A _Andrew Howroyd_, Jan 25 2020
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