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Search: id:A052365
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| A052365 |
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Number of nonnegative integer 3 X 3 matrices with sum of elements equal to n, under row and column permutations. |
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+0
7
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| 1, 1, 4, 10, 24, 51, 114, 219, 424, 768, 1352, 2278, 3759, 5978, 9328, 14181, 21164, 30943, 44560, 63063, 88088, 121321, 165152, 222157, 295857, 389948, 509456, 659697, 847552, 1080452, 1367814, 1719652, 2148596, 2668107, 3294676, 4046069
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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.
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LINKS
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G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
Index entries for Molien series
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FORMULA
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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).
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);
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CROSSREFS
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Cf. A002724, A053307, A052366, A052267, A092091.
Sequence in context: A128516 A022569 A093831 this_sequence A107659 A162588 A080615
Adjacent sequences: A052362 A052363 A052364 this_sequence A052366 A052367 A052368
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 08 2000
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