A051528 Molien series for group G_{1,2} of order 384.

1, 0, 0, 0, 4, 2, 3, 2, 11, 7, 11, 9, 25, 18, 27, 23, 48, 38, 54, 47, 83, 69, 94, 84, 133, 114, 150, 136, 200, 176, 225, 206, 287, 257, 321, 297, 397, 360, 441, 411, 532, 488, 588, 551, 695, 643, 764, 720, 889, 828, 972, 920, 1116, 1046, 1215

Offset

0,5

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

E. Bannai, S. T. Dougherty, M. Harada and M. Oura, Type II Codes, Even Unimodular Lattices and Invariant Rings, IEEE Trans. Information Theory, Volume 45, Number 4, 1999, 1194-1205.

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,1,-1,-1,1,-2,2,0,0,1,-1).

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=4, a(5)=2, a(6)=3, a(7)=2, a(8)=11, a(9)=7, a(10)=11, a(11)=9, a(12)=25, a(13)=18, a(14)=27, a(n)=a(n-1)+ 2*a(n-4)- 2*a(n-5)+ a(n-6)- a(n-7)-a(n-8)+a(n-9)-2*a(n-10)+ 2*a(n-11)+ a(n-14)-a(n-15). - Harvey P. Dale, Mar 04 2013

a(n) ~ 1/144*n^3. - Ralf Stephan, May 17 2014

G.f.: (x^12-x^9+2*x^8+2*x^4-x+1) / ((x-1)^4*(x+1)^3*(x^2-x+1)*(x^2+1)^2*(x^2+x+1)). - Colin Barker, Apr 02 2015

Maple

(1+x)*(1+x^2)*(1-x+2*x^4+2*x^8-x^9+x^12)/((1-x^4)^3*(1-x^6));

Mathematica

CoefficientList[Series[(1+x)*(1+x^2)*(1-x+2*x^4+2*x^8-x^9+x^12)/((1-x^4)^3*(1-x^6)), {x, 0, 60}], x] (* or *) LinearRecurrence[ {1, 0, 0, 2, -2, 1, -1, -1, 1, -2, 2, 0, 0, 1, -1}, {1, 0, 0, 0, 4, 2, 3, 2, 11, 7, 11, 9, 25, 18, 27}, 60] (* Harvey P. Dale, Mar 04 2013 *)

Prog

(PARI) Vec((x^12-x^9+2*x^8+2*x^4-x+1)/((x-1)^4*(x+1)^3*(x^2-x+1)*(x^2+1)^2*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Apr 02 2015

Crossrefs

Sequence in context: A079636 A308261 A019614 * A073244 A106644 A345996

Adjacent sequences: A051525 A051526 A051527 * A051529 A051530 A051531

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved