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

0,2

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

Table of n, a(n) for n=0..20.

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

Formula

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

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

Status

approved