Search: id:A052365
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%I A052365
%S A052365 1,1,4,10,24,51,114,219,424,768,1352,2278,3759,5978,9328,14181,21164,
%T A052365 30943,44560,63063,88088,121321,165152,222157,295857,389948,509456,
%U A052365 659697,847552,1080452,1367814,1719652,2148596,2668107,3294676,4046069
%N A052365 Number of nonnegative integer 3 X 3 matrices with sum of elements equal 
               to n, under row and column permutations.
%C A052365 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 A052365 G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://www.research.att.com/
               ~njas/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, 
               Springer, Berlin, 2006.
%H A052365 <a href="Sindx_Mo.html#Molien">Index entries for Molien series</a>
%F A052365 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 A052365 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 A052365 Cf. A002724, A053307, A052366, A052267, A092091.
%Y A052365 Sequence in context: A128516 A022569 A093831 this_sequence A107659 A162588 
               A080615
%Y A052365 Adjacent sequences: A052362 A052363 A052364 this_sequence A052366 A052367 
               A052368
%K A052365 nonn
%O A052365 0,3
%A A052365 Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 08 2000

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