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.

1, 12, 124, 1280, 13456, 143808, 1556416, 17006592, 187207936, 2072947712, 23063919616, 257634271232, 2887544049664, 32456082440192, 365710391885824, 4129672996585472, 46721752249729024, 529486122704437248, 6009576477811277824, 68299997524116111360

Offset: 1

Author

Andrew Howroyd, Jan 15 2020

Keywords

• nonn

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

Crossrefs

Column k=2 of A331278.

Cf. A011782, A047665, A052141, A331397.

Programs

PARI

seq(n)={Vec(1/(4*sqrt(1 - 12*x + 4*x^2 + O(x*x^n))) - 1/(4*(1-2*x)))}

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).