A058408 Number of 3 X n nonnegative integer matrices with all column sums 4, up to row and column permutation.

1, 4, 26, 129, 546, 2010, 6615, 19650, 53790, 137035, 328262, 745078, 1613072, 3348198, 6693822, 12937656, 24253200, 44219610, 78604130, 136511100, 232054284, 386737802, 632819628, 1017983052, 1611768873, 2514310812, 3868112340, 5873727245, 8810503300, 13063741460, 19160026567

Offset

0,2

Comments

Number of 3 X n nonnegative integer matrices with all column sums equal to m, up to row and column permutation, is coefficient of x^n in expansion of 1 / 6 * (1 / (1 - x)^C(m + 2,2) + 3 / (1 - x)^floor((m + 2) / 2) / (1 - x^2)^(C(m + 2,2) - floor((m + 2) / 2)) / 2 + 2 / (1 - x)^(C(m + 2,2) - 3 * floor(C(m + 2,2) / 3)) / (1 - x^3)^floor(C(m + 2,2) / 3)).

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10000

Number of m x l nonnegative integer matrices with all column sums equal to n, up to row and column permutation

Index entries for linear recurrences with constant coefficients, signature (4,0,-15,0,36,26, -80,-90,110,196,-54, -325,-80,360,245,-245, -360,80,325,54,-196, -110,90,80,-26, -36,0,15,0,-4,1).

Formula

G.f.: 1/6*(1/(1-x)^15+3/(1-x)^3/(1-x^2)^6+2/(1-x^3)^5).

Prog

(PARI) seq(n)=Vec(1/6*(1/(1-x)^15+3/(1-x)^3/(1-x^2)^6+2/(1-x^3)^5) + O(x*x^n)) \\ Andrew Howroyd, Oct 30 2025

Crossrefs

Cf. A050531, A058389, A058407.

Sequence in context: A261738 A363648 A184263 * A053906 A359962 A316539

Adjacent sequences: A058405 A058406 A058407 * A058409 A058410 A058411

Keyword

easy,nonn

Author

Vladeta Jovovic, Nov 25 2000

Extensions

a(21) onward from Andrew Howroyd, Oct 30 2025

Status

approved