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).

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

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 Molien series

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<x>:=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.<x> = 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: A362173 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