A058407 Number of 3 X n nonnegative integer matrices with all column sums 3, up to row and column permutation.

1, 3, 13, 44, 134, 356, 876, 1966, 4146, 8236, 15592, 28252, 49357, 83377, 136837, 218728, 341554, 522064, 782810, 1153180, 1671698, 2387568, 3363738, 4679208, 6433183, 8748119, 11775343, 15699188, 20744108, 27180308, 35332850, 45588746

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..31.

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)^10+3/(1-x)^2/(1-x^2)^4+2/(1-x)/(1-x^3)^3).

Crossrefs

Cf. A050531, A058389, A058408.

Sequence in context: A284194 A209296 A193041 * A095863 A136520 A212416

Adjacent sequences: A058404 A058405 A058406 * A058408 A058409 A058410

Keyword

easy,nonn

Author

Vladeta Jovovic, Nov 25 2000

Extensions

More terms from Max Alekseyev, Jun 21 2011

Status

approved