A092070 Molien series for genus 2 complete weight enumerators of self-dual codes over GF(3) containing the all-ones vector.

1, 2, 13, 87, 472, 2099, 7651, 23632, 64007, 155869, 347888, 722562, 1412787, 2623960, 4663042, 7975064, 13188959, 21174366, 33109962, 50565794, 75601497, 110881127, 159807508, 226678408, 316865230, 437017617, 595296931, 801638887, 1068049576, 1408938228

Offset

0,2

Comments

The invariant ring for a 9-dimensional group Z_4 X 3^{1+4}_{+}.SP_4(3) of order 50388480.

Links

Table of n, a(n) for n=0..29.

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 (3,-2,1,-6,7,-3,4,-5,7,-5,-4,0,4,5,-7,5,-4,3,-7,6,-1,2,-3,1).

Maple

# (Maple code for Molien series:)
f := 1+8*t^2+60*t^3+292*t^4+1090*t^5+3127*t^6+7116*t^7 +13411*t^8 + 21536*t^9+29963*t^10+36631*t^11+39638*t^12 +37973*t^13+32135*t^14+ 23906*t^15+15462*t^16+8507*t^17 +3858*t^18+1369*t^19+342*t^20+52*t^21+3*t^22;
u1 := subs(t=t^12, f); u2 := (1-t^12)^2*(1-t^24)^2*(1-t^36)^3*(1-t^60)^2; MS := u1/u2;
seq(coeff(series(MS, t, 12*n+3), t, 12*n), n=0..30);

Mathematica

CoefficientList[Series[(1+8*x^2+60*x^3+292*x^4+1090*x^5+3127*x^6+7116*x^7 +13411*x^8 + 21536*x^9+29963*x^10+36631*x^11+39638*x^12 +37973*x^13+32135*x^14+ 23906*x^15+15462*x^16+8507*x^17 +3858*x^18+1369*x^19+342*x^20+52*x^21+3*x^22) / (-(x+1)^2*(x^4+x^3+x^2+x+1)^2*(x^2+x+1)^3*(x-1)^9), {x, 0, 28}], x] (* Georg Fischer, Jan 25 2021 *)

Crossrefs

Sequence in context: A164035 A074619 A162275 * A091116 A091099 A092849

Adjacent sequences: A092067 A092068 A092069 * A092071 A092072 A092073

Keyword

nonn

Author

N. J. A. Sloane, Mar 30 2004

Status

approved