A331397 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, 2, 14, 128, 1288, 13472, 143840, 1556480, 17006720, 187208192, 2072948224, 23063920640, 257634273280, 2887544053760, 32456082448384, 365710391902208, 4129672996618240, 46721752249794560, 529486122704568320, 6009576477811539968, 68299997524116635648

Offset

0,2

Comments

The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Formula

a(n) = (A052141(n) + A011782(n))/2.

G.f.: 1/(4*sqrt(1 - 12*x + 4*x^2)) + (3 - 4*x)/(4*(1-2*x)).

a(n) = A011782(n) * A226994(n).

D-finite with recurrence n*a(n) +2*(-8*n+5)*a(n-1) +28*(2*n-3)*a(n-2) +8*(-8*n+19)*a(n-3) +16*(n-3)*a(n-4)=0. - R. J. Mathar, Mar 13 2023

Prog

(PARI) seq(n)={Vec(1/(4*sqrt(1 - 12*x + 4*x^2 + O(x*x^n))) + (3 - 4*x)/(4*(1-2*x)))} \\ Andrew Howroyd, Jan 15 2020

Crossrefs

Column k=2 of A331315.

Cf. A011782, A052141, A226994, A331396.

Sequence in context: A121082 A216595 A155650 * A363983 A258389 A168658

Adjacent sequences: A331394 A331395 A331396 * A331398 A331399 A331400

Keyword

nonn

Author

Andrew Howroyd, Jan 15 2020

Status

approved