%I #16 Jan 30 2018 18:57:34

%S 1,0,0,0,0,0,0,1,1,0,1,2,1,0,0,2,2,0,1,2,1,0,1,3,2,0,2,4,2,0,1,4,3,0,

%T 2,4,2,0,2,5,3,0,3,6,3,0,2,6,4,0,3,6,3,0,3,7,4,0,4,8,4,0,3,8,5,0,4,8,

%U 4,0,4,9,5,0,5,10,5,0,4,10,6,0,5,10,5,0,5,11,6,0,6,12,6,0,5,12,7,0,6,12,6,0

%N Poincaré series [or Poincare series] (or Molien series) for H*(M_11, GF(3)) and H*(M_23, GF(3)).

%D D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 107.

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-3,2,-1).

%F G.f.: ( 1 -3*x^7 +3*x^8 -2*x^15 +x^16-2*x -3*x^9 +3*x^2 +3*x^14 -4*x^3 +4*x^4 -4*x^5 +4*x^6 +4*x^10 -4*x^11 +4*x^12 -4*x^13 ) / ( (1+x^4)*(x^8+1)*(x-1)^2*(x^2+1)^2 ). - _R. J. Mathar_, Dec 18 2014

%p 1/2*((1+x^3)*(1+x^4)*(1+x^7)*(1+x^8)+(1-x^3)*(1-x^4)*(1-x^7)*(1-x^8))/(1-x^8)/(1-x^16)

%t LinearRecurrence[{2,-3,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-3,2,-1},{1,0,0,0,0,0,0,1,1,0,1,2,1,0,0,2,2,0},102]

%t (* _Ray Chandler_, Jul 15 2015 *)

%K nonn,easy

%O 0,12

%A _N. J. A. Sloane_