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 A092091 Molien series for 9-dimensional group of structure Z_2 X Z_2 and order 4, corresponding to complete weight enumerators of Hermitian self-dual GF(3)-linear codes over GF(9). 2
 1, 4, 17, 52, 147, 360, 819, 1712, 3382, 6312, 11286, 19368, 32154, 51744, 81114, 124080, 185823, 272844, 393679, 558844, 781781, 1078792, 1470261, 1980576, 2639676, 3482960, 4553212, 5900496, 7584516, 9674496, 12252036, 15410976, 19260813, 23926548, 29552733 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006. Index entries for linear recurrences with constant coefficients, signature (5,-6,-10,29,-9,-36,36,9,-29,10,6,-5,1). FORMULA G.f.: (1 +2*x^2 +4*x^3 +x^4)/((1-x)^4*(1-x^2)^5). G.f.: (1 -x +3*x^2 +x^3)/( (1+x)^4*(1-x)^9 ). - R. J. Mathar, Dec 18 2014 a(n) = ((315*(857+167*(-1)^n) + 60*(8347+581*(-1)^n)*n + (384718+6930*(-1)^n)*n^2 + 84*(2027+5*(-1)^n)*n^3 + 48888*n^4 + 9240*n^5 + 1092*n^6 + 72*n^7 + 2*n^8)) / 322560. - Colin Barker, Jan 16 2017 MAPLE seq(coeff(series((1-x+3*x^2+x^3)/((1+x)^4*(1-x)^9), x, n+1), x, n), n = 0..40); # G. C. Greubel, Feb 02 2020 MATHEMATICA LinearRecurrence[{5, -6, -10, 29, -9, -36, 36, 9, -29, 10, 6, -5, 1}, {1, 4, 17, 52, 147, 360, 819, 1712, 3382, 6312, 11286, 19368, 32154}, 35] (* Ray Chandler, Jul 15 2015 *) PROG (PARI) Vec((1 -x +3*x^2 +x^3)/((1-x)^9*(1+x)^4) + O(x^40)) \\ Colin Barker, Jan 16 2017 (MAGMA) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x+3*x^2+x^3)/((1+x)^4*(1-x)^9) )); // G. C. Greubel, Feb 02 2020 (Sage) def A092091_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( (1-x+3*x^2+x^3)/((1+x)^4*(1-x)^9) ).list() A092091_list(40) # G. C. Greubel, Feb 02 2020 (GAP) List([0..40], n-> ((315*(857 +167*(-1)^n) +60*(8347 +581*(-1)^n)*n + (384718 +6930*(-1)^n)*n^2 +84*(2027 +5*(-1)^n)*n^3 +48888*n^4 +9240*n^5 +1092*n^6 +72*n^7 +2*n^8))/322560 ); # G. C. Greubel, Feb 02 2020 CROSSREFS Cf. A052365. Sequence in context: A131339 A047668 A208658 * A046995 A001585 A060262 Adjacent sequences:  A092088 A092089 A092090 * A092092 A092093 A092094 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Apr 01 2004 STATUS approved

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Last modified May 10 21:08 EDT 2021. Contains 343780 sequences. (Running on oeis4.)