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%I #12 Jan 23 2020 14:44:26
%S 1,12,124,1280,13456,143808,1556416,17006592,187207936,2072947712,
%T 23063919616,257634271232,2887544049664,32456082440192,
%U 365710391885824,4129672996585472,46721752249729024,529486122704437248,6009576477811277824,68299997524116111360
%N Number of nonnegative integer matrices with 2 distinct columns and any number of nonzero rows with column sums n and columns in decreasing lexicographic order.
%C The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.
%H Andrew Howroyd, <a href="/A331396/b331396.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = (A052141(n) - A011782(n))/2.
%F G.f.: 1/(4*sqrt(1 - 12*x + 4*x^2)) - 1/(4*(1-2*x)).
%F a(n) = A011782(n) * A047665(n).
%o (PARI) seq(n)={Vec(1/(4*sqrt(1 - 12*x + 4*x^2 + O(x*x^n))) - 1/(4*(1-2*x)))}
%Y Column k=2 of A331278.
%Y Cf. A011782, A047665, A052141, A331397.
%K nonn
%O 1,2
%A _Andrew Howroyd_, Jan 15 2020
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