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

1,2

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