|
| |
|
|
A092069
|
|
Molien series for genus 2 complete weight enumerators of self-dual codes over GF(3).
|
|
0
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
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
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
