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 A052365 Number of nonnegative integer 3 X 3 matrices with sum of elements equal to n, under row and column permutations. 8

%I

%S 1,1,4,10,24,51,114,219,424,768,1352,2278,3759,5978,9328,14181,21164,

%T 30943,44560,63063,88088,121321,165152,222157,295857,389948,509456,

%U 659697,847552,1080452,1367814,1719652,2148596,2668107,3294676,4046069

%N Number of nonnegative integer 3 X 3 matrices with sum of elements equal to n, under row and column permutations.

%C Also Molien series for group of structure S_3 X S_3 = (Z_3 X Z_3).O_2^+(3) and order 36, corresponding to complete weight enumerators of Hermitian self-dual GF(3)-linear codes over GF(9) containing the all-ones vector.

%H Andrew Howroyd, <a href="/A052365/b052365.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.

%H <a href="/index/Mo#Molien">Index entries for Molien series</a>

%F G.f.: -(x^10+2*x^8+x^7+7*x^6-3*x^5+4*x^3+x^2-2*x+1) / ((x^4-x^3+x-1)*(x^3-1)^3*(x+1)^3*(x-1)^5).

%F Another form for g.f.: u1/u2, where u1 := 1 + x + 2*x^3 + 10*x^4 + 17*x^5 + 19*x^6 + 20*x^7 + 29*x^8 + 37*x^9 + 34*x^10 + 23*x^11 + 12*x^12 + 7*x^13 + 3*x^14 + x^15 u2 := (1-x^2)^4*(1-x^3)^4*(1-x^6);

%Y Row 3 of A318795.

%Y Cf. A002724, A053307, A052366, A052267, A092091.

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Mar 08 2000

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Last modified May 22 05:03 EDT 2019. Contains 323473 sequences. (Running on oeis4.)