%I #4 Jan 25 2020 20:55:12
%S 0,1,46,1900,73028,2448599,75497242,2339274204,69674762468,
%T 1979828352817,54476556180342,1451352388018928,37417987990316376,
%U 936855054326483475,22833066202591181758,542259452432969505704,12569324678536063256324,284784345516356806067001,6313245421002223574950650
%N Number of nonnegative integer matrices with 3 distinct columns and any number of distinct 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.
%e The a(1) = 1 matrix is:
%e [1 0 0]
%e [0 1 0]
%e [0 0 1]
%Y Column k=3 of A331570.
%Y Cf. A331706.
%K nonn
%O 0,3
%A _Andrew Howroyd_, Jan 25 2020