cp's OEIS Frontend

A168992 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

%I A168992 #10 Nov 25 2016 10:26:21
%S A168992 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A168992 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A168992 2576581829865418752,66991127576500887552,1741769316989023076352
%N A168992 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
%C A168992 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A168992 First disagreement at index 23: a(23) = 363728573635362135848513282506401, A170746(23) = 363728573635362135848513282506752. - Klaus Brockhaus, Apr 19 2011
%C A168992 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168992 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
%F A168992 G.f.: (t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(325*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
%t A168992 With[{num=Total[2t^Range[22]]+t^23+1,den=Total[-25 t^Range[22]]+ 325t^23+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Dec 10 2012 *)
%Y A168992 Cf. A170746 (G.f.: (1+x)/(1-26*x)).
%K A168992 nonn
%O A168992 0,2
%A A168992 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009