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%I #16 Jan 30 2018 18:57:36
%S 1,0,1,3,0,2,5,0,3,7,0,4,9,0,5,11,0,6,13,0,7,15,0,8,17,0,9,19,0,10,21,
%T 0,11,23,0,12,25,0,13,27,0,14,29,0,15,31,0,16,33,0,17,35,0,18,37,0,19,
%U 39,0,20,41,0,21,43,0,22,45,0,23,47,0,24,49,0,25,51,0,26,53,0,27,55,0,28,57
%N G.f.: (1+x^2+x^3)/(1-x^3)^2.
%C Poincaré series [or Poincare series] (or Molien series) for F_4[x_1, y_1]^{Z/3}.
%D A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 91.
%H Harvey P. Dale, <a href="/A089598/b089598.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F a(0)=1, a(1)=0, a(2)=1, a(3)=3, a(4)=0, a(5)=2, a(n)=2*a(n-3)-a(n-6). - _Harvey P. Dale_, May 20 2012
%t CoefficientList[Series[(1+x^2+x^3)/(1-x^3)^2,{x,0,90}],x] (* or *) LinearRecurrence[{0,0,2,0,0,-1},{1,0,1,3,0,2},90] (* _Harvey P. Dale_, May 20 2012 *)
%Y Cf. A005408 (trisection), A000027 (trisection).
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Dec 31 2003
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