This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091972 #22 Aug 26 2025 21:32:34
%S A091972 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 A091972 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 A091972 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 A091972 Expansion of g.f. (1 + x^5 ) / ( (1-x^3)*(1-x^4)).
%C A091972 Poincaré series [or Poincare series] (or Molien series) for Mathieu group M_11.
%D A091972 A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 247.
%H A091972 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,2,-1,1,-1).
%F A091972 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) for n > 5. - _Harvey P. Dale_, Dec 11 2012
%F A091972 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
%F A091972 E.g.f.: (3*exp(x)*(1 + x) + 9*cos(x) + exp(-x/2)*(6*cos(sqrt(3)*x/2) - 2*sqrt(3)*sin(sqrt(3)*x/2)))/18. - _Stefano Spezia_, Aug 26 2025
%t A091972 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 A091972 nonn,easy,changed
%O A091972 0,9
%A A091972 _N. J. A. Sloane_, Mar 18 2004