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%I #15 Dec 27 2023 13:51:32
%S 1,0,0,1,0,1,1,0,2,2,1,2,3,2,3,5,3,5,6,4,8,8,6,10,12,10,12,15,13,17,
%T 19,16,23,24,21,28,30,28,33,37,36,41,44,42,51,54,50,60,65,62,70,75,74,
%U 83,87,86,98,102,99,112,119,116,127,135,135,147,152,152,168,174,172,188,198,196
%N G.f.: ((1 + x^9)*(1 + x^(15)) ) / ( (1 - x^3)*(1 - x^5)*(1 - x^8)*(1 - x^(12))).
%C Poincaré series [or Poincare series] (or Molien series) for F_2[x_1..x_4]^(A_6).
%D A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004, last page of Chapter III.
%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (1, -1, 3, -3, 4, -6, 6, -7, 9, -9, 9, -10, 9, -9, 9, -7, 6, -6, 4, -3, 3, -1, 1, -1).
%F G.f.: (1-x+x^2) *(x^4-x^3+x^2-x+1) *(x^6-x^3+1) *(x^8+x^7-x^5-x^4-x^3+x+1) / ( (x^4+x^3+x^2+x+1) *(x^4-x^2+1) *(x^4+1) *(x^2+1)^2 *(1+x+x^2)^2 *(x-1)^4 ). - _R. J. Mathar_, Dec 18 2014
%t CoefficientList[Series[((1+x^9)(1+x^(15)))/((1-x^3)(1-x^5)(1-x^8)(1-x^(12))),{x,0,80}],x] (* or *) LinearRecurrence[{1,-1,3,-3,4,-6,6,-7,9,-9,9,-10,9,-9,9,-7,6,-6,4,-3,3,-1,1,-1},{1,0,0,1,0,1,1,0,2,2,1,2,3,2,3,5,3,5,6,4,8,8,6,10},80] (* _Harvey P. Dale_, Dec 27 2023 *)
%o (PARI) Vec(((1 + x^9)*(1 + x^(15)))/((1 - x^3)*(1 - x^5)*(1 - x^8)*(1 - x^(12))) + O(x^80)) \\ _Jinyuan Wang_, Mar 10 2020
%K nonn,easy
%O 0,9
%A _N. J. A. Sloane_, Mar 16 2004
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