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Molien series for group H_{1,3} of order 1152.
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%I #20 Jul 31 2015 11:16:32

%S 1,0,1,3,4,5,15,14,24,35,44,54,81,88,115,143,168,195,247,270,322,375,

%T 424,476,561,608,693,779,860,945,1071,1150,1276,1403,1524,1650,1825,

%U 1944,2119,2295,2464,2639,2871,3038,3270,3503,3728,3960,4257,4480

%N Molien series for group H_{1,3} of order 1152.

%H E. Bannai, S. T. Dougherty, M. Harada and M. Oura, <a href="https://sites.google.com/site/professorstevendougherty/publications">Type II Codes, Even Unimodular Lattices and Invariant Rings</a>, IEEE Trans. Information Theory, Volume 45, Number 4, 1999, 1194-1205.

%H <a href="/index/Mo#Molien">Index entries for Molien series</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, -1, -1, 2, -1, -1, 0, 1, 1, -1).

%F G.f.: (x^9+x^8-x^7+5*x^6-x^5+x^4+2*x^3-x+1)/((x-1)^4*(x+1)^2*(x^2+x+1)^2*(x^2-x+1)).

%F a(0)=1, a(1)=0, a(2)=1, a(3)=3, a(4)=4, a(5)=5, a(6)=15, a(7)=14, a(8)=24, a(9)=35, a(10)=44, a(11)=54, a(n)=a(n-1)+a(n-2)-a(n-4)-a(n-5)+ 2*a(n-6)-a(n-7)-a(n-8)+a(n-10)+a(n-11)-a(n-12). - _Harvey P. Dale_, Jun 15 2013

%F a(n) ~ 1/27 * n^3. - _Ralf Stephan_, May 17 2014

%t CoefficientList[Series[(x^9+x^8-x^7+5x^6-x^5+x^4+2x^3-x+1)/((x-1)^4 (x+1)^2(x^2+x+1)^2(x^2-x+1)),{x,0,50}],x] (* or *) LinearRecurrence[ {1,1,0,-1,-1,2,-1,-1,0,1,1,-1},{1,0,1,3,4,5,15,14,24,35,44,54},50] (* _Harvey P. Dale_, Jun 15 2013 *)

%K nonn,easy,nice

%O 0,4

%A _N. J. A. Sloane_

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 15 2001