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%I #11 Jan 16 2024 22:04:53
%S 1,3,13,38,97,217,453,868,1585,2756,4606,7440,11679,17849,26674,39060,
%T 56144,79387,110575,151904,206063,276332,366561,481484,626586,808431,
%U 1034636,1314242,1657500,2076601,2585262,3199504,3937370,4819788
%N Number of nonnegative integer 3 X 3 matrices with no zero rows or columns and with sum of elements equal to n, up to row and column permutation.
%H Andrew Howroyd, <a href="/A054975/b054975.txt">Table of n, a(n) for n = 3..1000</a>
%F G.f.: x^3*(x^14 - 2*x^13 + x^12 - 3*x^11 + 4*x^10 - 3*x^9 + 4*x^8 - x^7 - 4*x^6 + 2*x^5 - x^4 - 5*x^3 - 4*x^2 - 1)/((x^4 - x^3 + x - 1)*(x^3 - 1)^3*(x + 1)^3*(x - 1)^5).
%e There are 3 nonnegative integer 3 X 3 matrices with no zero rows or columns and with sum of elements equal to 4, up to row and column permutation:
%e [0 0 1] [0 0 1] [0 0 1]
%e [0 0 1] [0 1 0] [0 1 0]
%e [1 1 0] [1 0 1] [2 0 0].
%p gf := x^3*(x^14 - 2*x^13 + x^12 - 3*x^11 + 4*x^10 - 3*x^9 + 4*x^8 - x^7 - 4*x^6 + 2*x^5 - x^4 - 5*x^3 - 4*x^2 - 1)/((x^4 - x^3 + x - 1)*(x^3 - 1)^3*(x+1)^3*(x - 1)^5): s := series(gf, x, 101): for i from 3 to 100 do printf(`%d,`,coeff(s,x,i)) od:
%Y Column k=3 of A321615.
%Y Cf. A052365.
%K easy,nonn
%O 3,2
%A _Vladeta Jovovic_, May 28 2000
%E More terms from _James A. Sellers_, May 29 2000
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