A091972 - OEIS

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

%S 1,0,0,1,1,1,1,1,2,2,1,2,3,2,2,3,3,3,3,3,4,4,3,4,5,4,4,5,5,5,5,5,6,6,

%T 5,6,7,6,6,7,7,7,7,7,8,8,7,8,9,8,8,9,9,9,9,9,10,10,9,10,11,10,10,11,

%U 11,11,11,11,12,12,11,12,13,12,12,13,13,13,13,13,14,14,13,14,15,14,14,15,15,15

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

%C Poincaré series [or Poincare series] (or Molien series) for Mathieu group M_11.

%D A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 247.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,2,-1,1,-1).

%F a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=1, a(5)=1, a(n)=a(n-1)-a(n-2)+ 2*a(n-3)- a(n-4)+a(n-5)-a(n-6). - _Harvey P. Dale_, Dec 11 2012

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

%t CoefficientList[Series[(1+x^5)/((1-x^3)(1-x^4)),{x,0,90}],x] (* or *) LinearRecurrence[{1,-1,2,-1,1,-1},{1,0,0,1,1,1},90] (* _Harvey P. Dale_, Dec 11 2012 *)

%K nonn,easy

%O 0,9

%A _N. J. A. Sloane_, Mar 18 2004