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

Offset: 0

Author

Vladeta Jovovic, Nov 25 2000

Keywords

• easy
• nonn

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

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

Crossrefs

Cf. A050531, A058389, A058407.

Formula

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