A092549 Molien series for symmetrized weight enumerators of self-dual codes over GF(4) + GF(4)u with u^2 = 0.

1, 1, 3, 3, 8, 9, 18, 20, 37, 42, 69, 78, 122, 139, 204, 231, 327, 371, 505, 570, 756, 852, 1100, 1234, 1563, 1749, 2173, 2421, 2964, 3293, 3974, 4398, 5247, 5790, 6831, 7512, 8782, 9631, 11160, 12201, 14033, 15303, 17475, 19004, 21568, 23400, 26400, 28572

Offset

0,3

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 (2,0,-2,3,-4,1,2,-3,4,-3,2,1,-4,3,-2,0,2,-1).

Formula

G.f.: (1+x^5+x^8+x^13)/((1-x)*(1-x^2)^2*(1-x^4)^2*(1-x^6)).

G.f.: (1-x+x^2-x^3+x^4)*(1+x^8) / ((1-x)^6*(1+x)^4*(1-x+x^2)*(1+x^2)^2*(1+x+x^2)). - Colin Barker, Apr 02 2015

Maple

seq(coeff(series((1+x^5+x^8+x^13)/((1-x)*(1-x^2)^2*(1-x^4)^2*(1-x^6)), x, n+1), x, n), n = 0..50); # G. C. Greubel, Feb 03 2020

Mathematica

CoefficientList[Series[(1+x^5+x^8+x^13)/((1-x)*(1-x^2)^2*(1-x^4)^2*(1-x^6)), {x, 0, 50}], x] (* G. C. Greubel, Feb 03 2020 *)

Prog

(PARI) Vec((x^4-x^3+x^2-x+1)*(x^8+1)/((x-1)^6*(x+1)^4*(x^2-x+1)*(x^2+1)^2*(x^2+x+1)) + O(x^50)) \\ Colin Barker, Apr 02 2015
(Sage)
def A092549_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x^5+x^8+x^13)/((1-x)*(1-x^2)^2*(1-x^4)^2*(1-x^6)) ).list()
A092549_list(50) # G. C. Greubel, Feb 03 2020

Crossrefs

Cf. A092548.

Sequence in context: A182473 A363125 A335602 * A260890 A022663 A304967

Adjacent sequences: A092546 A092547 A092548 * A092550 A092551 A092552

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 09 2004

Extensions

Corrected by G. Nebe, Jun 30 2005

Status

approved