%I #14 Jan 30 2018 18:57:37

%S 1,0,0,1,1,2,2,1,3,4,4,5,5,6,8,9,9,10,12,13,15,16,16,19,21,22,24,25,

%T 27,30,32,33,35,38,40,43,45,46,50,53,55,58,60,63,67,70,72,75,79,82,86,

%U 89,91,96,100,103,107,110,114,119,123,126,130,135,139,144,148,151,157,162,166

%N G.f.: (1+x^3)*(1+x^5)*(1+x^6)/((1-x^4)*(1-x^5)*(1-x^6)).

%C Let G = G_2(q) or ^3D_4(q) with q == 1 mod 4. The Poincaré series [or Poincare series] (or Molien series) for G is independent of q and is given here.

%D A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 242.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,1,-1,0,-1,1).

%F G.f.: -(x^4-x^3+x^2-x+1)*(x^4-x^2+1) / ( (1+x+x^2)*(x^4+x^3+x^2+x+1)*(x-1)^3 ). - _R. J. Mathar_, Sep 27 2014

%t CoefficientList[Series[(1+x^3)*(1+x^5)*(1+x^6)/((1-x^4)*(1-x^5)*(1-x^6)),{x,0,80}],x] (* or *) LinearRecurrence[{1,0,1,-1,1,-1,0,-1,1},{1,0,0,1,1,2,2,1,3},80] (* _Harvey P. Dale_, Feb 19 2017 *)

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_, Mar 15 2004