A028345 Molien series for complete weight enumerator of self-dual code over GF(5) containing all-1's vector.

1, 1, 6, 21, 48, 112, 224, 390, 656, 1037, 1545, 2245, 3158, 4300, 5757, 7554, 9713, 12339, 15463, 19111, 23409, 28392, 34092, 40654, 48119, 56523, 66032, 76691, 88542, 101770, 116426, 132556, 150366, 169911, 191243, 214587, 240004, 267550, 297471, 329832, 364695

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2,0,0,-3,0,3,0,0,-2,1).

Formula

Aerated g.f.: -(2*t^80 + 2*t^70 + 15*t^60 + 19*t^50 + 9*t^40 + 9*t^30 + 4*t^20 - t^10 + 1)/( t^100 - 2*t^90 + 3*t^60 - 3*t^40 + 2*t^10 - 1).

G.f.: (1 - x + 4*x^2 + 9*x^3 + 9*x^4 + 19*x^5 + 15*x^6 + 2*x^7 + 2*x^8)/((1 - x)^5*(1 + x)*(1 + x + x^2)^2). - Andrew Howroyd, Nov 02 2025

Mathematica

Take[CoefficientList[Series[(-2*t^80 - 2*t^70 - 15*t^60 - 19*t^50 - 9*t^40 - 9*t^30 - 4*t^20 + t^10 - 1)/(t^100 - 2*t^90 + 3*t^60 - 3*t^40 + 2*t^10 - 1), {t, 0, 10000}], t], {1, -1, 10}] (* G. C. Greubel, Nov 25 2016 *)

Crossrefs

Sequence in context: A213388 A372226 A163715 * A357691 A341985 A341066

Adjacent sequences: A028342 A028343 A028344 * A028346 A028347 A028348

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved