A099720 - OEIS

A099720

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

1, 1, 1, 3, 9, 9, 19, 45, 145, 260, 604, 1354, 3182, 6298, 13020, 25642, 50388, 92820, 170578, 303424, 533798, 908606, 1530476, 2522074, 4107717, 6553695, 10343897, 16070605, 24706363, 37437245, 56184469, 83316627, 122439255, 177978716, 256574818, 366404272

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..35.

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) + t^72*f(t^-1), u2 := (1-t)*(1-t^3)*(1-t^4)^5*(1-t^6)^4*(1-t^8)^5 and

f(t) = 1+t^3 + t^4 + 4*t^6 + 15*t^7 + 75*t^8 + 101*t^9 + 274*t^10 + 555*t^11 + 1232*t^12 +2187*t^13 + 4122*t^14 + 7245*t^15 + 12514*t^16 + 20155*t^17 + 31998*t^18 + 48747*t^19 + 72408*t^20 + 103925*t^21 +

144878*t^22 + 197573*t^23 + 261102*t^24 + 338155*t^25 + 425254*t^26 + 524445*t^27 + 629888*t^28 + 740973*t^29 + 851614*t^30 + 957155*t^31 + 1053412*t^32 + 1133809*t^33 + 1196064*t^34 + 1233375*t^35 + 1247150/2*t^36.

CROSSREFS

Sequence in context: A143225 A223195 A203600 * A183149 A223933 A224057

Adjacent sequences: A099717 A099718 A099719 * A099721 A099722 A099723

KEYWORD

nonn

AUTHOR

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

STATUS

approved