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A051528 Molien series for group G_{1,2} of order 384. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A087229 A308261 A019614 * A073244 A106644 A190874

Adjacent sequences:  A051525 A051526 A051527 * A051529 A051530 A051531

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)