A092069 Molien series for genus 2 complete weight enumerators of self-dual codes over GF(3).

1, 1, 1, 11, 35, 70, 278, 765, 1526, 3774, 8105, 14633, 28560, 51983, 85609, 145591, 237609, 364095, 565831, 855788, 1240383, 1808777, 2587237, 3590112, 4992854, 6844101, 9172450, 12296446, 16300139, 21235896, 27646466, 35669378, 45394358, 57699934, 72801345

Offset

0,4

Comments

The invariant ring for a 9-dimensional group Z_4 X SP_4(3) of order 207360.

These are the coefficients of the expansion in powers of t^4, the other coefficients being zero. - Georg Fischer, Jan 24 2021

Links

Table of n, a(n) for n=0..34.

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 (0,1,4,0,-2,-6,-2,-2,6,7,6,-8,-8,-3,8,6,6,-3,-12,-15,0,15,12,3,-6,-6,-8,3,8,8, -6,-7,-6,2,2,6,2,0,-4,-1,0,1).

Formula

O.g.f.: (1 + t^4 + 6*t^12 + 30*t^16 + 57*t^20 + 207*t^24 + 565*t^28 + 1000*t^32 + 2031*t^36 + 3880*t^40 + 5804*t^44 + 8696*t^48 + 12991*t^52 + 16595*t^56 + 20527*t^60 + 25965*t^64 + 29418*t^68 + 31536*t^72 + 34772*t^76 + 35273*t^80 + 33093*t^84 + 31969*t^88 + 29068*t^92 + 23862*t^96 + 20052*t^100 + 16217*t^104 + 11369*t^108 + 7996*t^112 + 5554*t^116 + 3097*t^120 + 1642*t^124 + 930*t^128 + 350*t^132 + 104*t^136 + 51*t^140 + 9*t^144 + t^148 + t^152) / ((1-t^36)^2 * (1-t^20)^2 * (1-t^12)^4 * (1-t^8)). - Georg Fischer, Jan 24 2021

Maple

# (Maple code for Molien series:)
u1 := 1 + t^4 + 6*t^12 + 30*t^16 + 57*t^20 + 207*t^24 + 565*t^28 + 1000*t^32 + 2031*t^36 + 3880*t^40 + 5804*t^44 + 8696*t^48 + 12991*t^52 + 16595*t^56 + 20527*t^60 + 25965*t^64 + 29418*t^68 + 31536*t^72 + 34772*t^76 + 35273*t^80
+ 33093*t^84 + 31969*t^88 + 29068*t^92 + 23862*t^96 + 20052*t^100 + 16217*t^104 + 11369*t^108 + 7996*t^112 + 5554*t^116 + 3097*t^120 + 1642*t^124 + 930*t^128 + 350*t^132 + 104*t^136 + 51*t^140 + 9*t^144 + t^148 + t^152;
u2 := (1-t^36)^2*(1-t^20)^2*(1-t^12)^4*(1-t^8); MS := u1/u2;
seq(coeff(series(MS, t, 4*n+3), t, 4*n), n=0..35);

Crossrefs

Sequence in context: A118554 A348845 A233546 * A103115 A003777 A222512

Adjacent sequences: A092066 A092067 A092068 * A092070 A092071 A092072

Keyword

nonn

Author

N. J. A. Sloane, Mar 30 2004

Status

approved