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A092546

Molien series for complete weight enumerators of Type II self-dual codes over Z/8Z.

1, 8, 185, 1837, 10404, 41956, 134424, 364816, 874316, 1901969, 3828391, 7231824, 12956547, 22195288, 36588651, 58340461, 90351150, 136372908, 201184234, 290786504, 412627262, 575846185, 791547105, 1073101792, 1436479605, 1900607176, 2487765101

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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), u2 = (1-x^8)^4*(1-x^16 )*(1-x^24 )^3, and f = 1 + 4*x + 158*x^2 + 1134*x^3 + 3964*x^4 + 9015*x^5 + 14318*x^6 + 16531*x^7 + 14322*x^8 + 9016 *x^9 + 3978 *x^10 + 1129 *x^11 + 155 *x^12 + 3 *x^13.

G.f.: (1 +4*x +158*x^2 +1134*x^3 +3964*x^4 +9015*x^5 +14318*x^6 +16531*x^7 +14322*x^8 +9016*x^9 +3978*x^10 +1129*x^11 +155*x^12 +3*x^13)/((1-x)^4*(1-x^2)*(1-x^3)^3). - G. C. Greubel, Feb 03 2020

MAPLE

f(x):= (1 +4*x +158*x^2 +1134*x^3 +3964*x^4 +9015*x^5 +14318*x^6 +16531*x^7 +14322*x^8 +9016*x^9 +3978*x^10 +1129*x^11 +155*x^12 +3*x^13)/((1-x)^4*(1-x^2)*(1-x^3)^3);

seq(coeff(series(f(x), x, n+1), x, n), n = 0..30); # G. C. Greubel, Feb 03 2020

MATHEMATICA

CoefficientList[Series[(1 +4*x +158*x^2 +1134*x^3 +3964*x^4 +9015*x^5 +14318*x^6 +16531*x^7 +14322*x^8 +9016*x^9 +3978*x^10 +1129*x^11 +155*x^12 +3*x^13)/((1-x)^4*(1-x^2)*(1-x^3)^3), {x, 0, 30}], x]

PROG

(PARI) Vec((1 +4*x +158*x^2 +1134*x^3 +3964*x^4 +9015*x^5 +14318*x^6 +16531*x^7 +14322*x^8 +9016*x^9 +3978*x^10 +1129*x^11 +155*x^12 +3*x^13)/((1-x)^4*(1-x^2)*(1-x^3)^3) +O('x^30) ) \\ G. C. Greubel, Feb 03 2020

CROSSREFS

Cf. A092545, A092546, A092547.

Sequence in context: A240319 A302913 A049034 * A227584 A197894 A198011

Adjacent sequences: A092543 A092544 A092545 * A092547 A092548 A092549

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 09 2004

STATUS

approved