

A058407


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


6



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



