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 A331396 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. 3
 1, 12, 124, 1280, 13456, 143808, 1556416, 17006592, 187207936, 2072947712, 23063919616, 257634271232, 2887544049664, 32456082440192, 365710391885824, 4129672996585472, 46721752249729024, 529486122704437248, 6009576477811277824, 68299997524116111360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 FORMULA a(n) = (A052141(n) - A011782(n))/2. G.f.: 1/(4*sqrt(1 - 12*x + 4*x^2)) - 1/(4*(1-2*x)). a(n) = A011782(n) * A047665(n). PROG (PARI) seq(n)={Vec(1/(4*sqrt(1 - 12*x + 4*x^2 + O(x*x^n))) - 1/(4*(1-2*x)))} CROSSREFS Column k=2 of A331278. Cf. A011782, A047665, A052141, A331397. Sequence in context: A016134 A045507 A288350 * A209041 A155595 A070312 Adjacent sequences:  A331393 A331394 A331395 * A331397 A331398 A331399 KEYWORD nonn AUTHOR Andrew Howroyd, Jan 15 2020 STATUS approved

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Last modified August 10 04:27 EDT 2022. Contains 356029 sequences. (Running on oeis4.)