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A058408 Number of 3 X n nonnegative integer matrices with all column sums 4, up to row and column permutation. 2

%I #6 May 10 2013 12:44:33

%S 1,4,26,129,546,2010,6615,19650,53790,137035,328262,745078,1613072,

%T 3348198,6693822,12937656,24253200,44219610,78604130,136511100,

%U 232054284

%N Number of 3 X n nonnegative integer matrices with all column sums 4, 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)^15+3/(1-x)^3/(1-x^2)^6+2/(1-x^3)^5).

%Y Cf. A050531, A058389, A058407.

%K easy,nonn

%O 0,2

%A _Vladeta Jovovic_, Nov 25 2000

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