A058407 - OEIS

%I #9 May 10 2013 12:44:33

%S 1,3,13,44,134,356,876,1966,4146,8236,15592,28252,49357,83377,136837,

%T 218728,341554,522064,782810,1153180,1671698,2387568,3363738,4679208,

%U 6433183,8748119,11775343,15699188,20744108,27180308,35332850,45588746

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

%C 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)).

%H <a href="/A058407/a058407.pdf">Number of m x l nonnegative integer matrices with all column sums equal to n, up to row and column permutation</a>

%F G.f.: 1/6*(1/(1-x)^10+3/(1-x)^2/(1-x^2)^4+2/(1-x)/(1-x^3)^3).

%Y Cf. A050531, A058389, A058408.

%K easy,nonn

%O 0,2

%A _Vladeta Jovovic_, Nov 25 2000

%E More terms from _Max Alekseyev_, Jun 21 2011