A099750 Molien series for complete weight enumerators of doubly-even Euclidean self-dual codes over the Galois ring GR(4,2).

1, 3, 22, 346, 5100, 53504, 411041, 2471091, 12244665, 51924492, 193733585, 649448814, 1988025385, 5628317525, 14888914321, 37110706136, 87756490312, 198017040530, 428428858514, 892492579595, 1796484842799, 3504861873102, 6645228329464, 12273264853180

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

S.-P. Eu, T.-S. Fu, Y.-J. Pan and C.-T. Ting, Baxter Permutations, Maj-balances, and Positive Braids, Electronic Journal of Combinatorics, 19(3) (2012), #P26. - From N. J. A. Sloane, Dec 25 2012

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 := f(t^4) + t^156*f(t^-4), u2 := (1-t^4)^3*(1-t^8)^5*(1-t^12)^5*(1-t^20)^3 and

f(t) = 1 + 11*t^2 + 283*t^3 + 4055*t^4 + 37722*t^5 + 243578*t^6 + 1179852*t^7 + 4535052*t^8 + 14380814*t^9 + 38708195*t^10 + 90379766*t^11 + 186147868*t^12 + 342605290*t^13 + 569177435*t^14 + 860160090*t^15+ 1189401593*t^16+ 1511365669*t^17+ 1770220838*t^18+ 1914917488*t^19.

Maple

f:= unapply(1 + 11*t^2 + 283*t^3 + 4055*t^4 + 37722*t^5 + 243578*t^6 + 1179852*t^7 + 4535052*t^8 + 14380814*t^9 + 38708195*t^10 + 90379766*t^11 + 186147868*t^12 + 342605290*t^13 + 569177435*t^14 + 860160090*t^15+ 1189401593*t^16+ 1511365669*t^17+ 1770220838*t^18+ 1914917488*t^19, t):
u1:= f(t) + t^39*f(t^(-1)):
u2:=  (1-t)^3*(1-t^2)^5*(1-t^3)^5*(1-t^5)^3:
S:= series(u1/u2, t, 51):
seq(coeff(S, t, j), j=0..50); # Robert Israel, May 02 2016

Crossrefs

Sequence in context: A002485 A360369 A193193 * A219268 A259919 A275366

Adjacent sequences: A099747 A099748 A099749 * A099751 A099752 A099753

Keyword

nonn

Author

G. Nebe (nebe(AT)math.rwth-aachen.de), Nov 10 2004

Status

approved