A092545 Molien series for complete weight enumerators of self-dual codes over Z/8Z containing the all-ones vector.

1, 3, 44, 361, 2010, 7952, 25401, 68662, 164459, 357241, 718934, 1357271, 2431460, 4164014, 6864051, 10942908, 16946805, 25576479, 37731200, 54532437, 77381198, 107985724, 148434413, 201227282, 269366687, 356392309, 466492202, 604540771

Offset

0,2

Links

G. C. Greubel, 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

Formula

G.f.: u1/u2 where u1 := subs(x=x^8, f); f := 1 + 35*x^2 + 237*x^3 + 943*x^4 + 2250*x^5 + 4089*x^6 + 5659*x^7 + 6323*x^8 + 5680*x^9 + 4057*x^10 + 2311*x^11 + 909*x^12 + 246*x^13 + 27*x^14 + x^15; u2 := (1-x^8)^3*(1-x^16 )^3*(1-x^32 )^2.

Maple

f(x):= (1 +35*x^2 +237*x^3 +943*x^4 +2250*x^5 +4089*x^6 +5659*x^7 +6323*x^8 +5680*x^9 +4057*x^10 +2311*x^11 +909*x^12 +246*x^13 + 27*x^14 +x^15)/((1-x)^3*(1-x^2)^3*(1-x^4)^2);
seq(coeff(series( f(x), x, n+1), x, n), n = 0..30); # G. C. Greubel, Feb 02 2020

Mathematica

CoefficientList[Series[(1 +35*x^2 +237*x^3 +943*x^4 +2250*x^5 +4089*x^6 +5659*x^7 +6323*x^8 +5680*x^9 +4057*x^10 +2311*x^11 +909*x^12 +246*x^13 + 27*x^14 +x^15)/((1-x)^3*(1-x^2)^3*(1-x^4)^2), {x, 0, 30}], x] (* G. C. Greubel, Feb 02 2020 *)

Crossrefs

Cf. A092544, A092545, A092546, A092547.

Sequence in context: A055539 A046946 A327360 * A353878 A359631 A011916

Adjacent sequences: A092542 A092543 A092544 * A092546 A092547 A092548

Keyword

nonn

Author

N. J. A. Sloane, Apr 09 2004

Status

approved