cp's OEIS Frontend

A169040 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

%I A169040 #10 Nov 25 2016 11:02:34
%S A169040 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A169040 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A169040 2576581829865418752,66991127576500887552,1741769316989023076352
%N A169040 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
%C A169040 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A169040 First disagreement at index 24: a(24) = 9456942914519415532061345345175201, A170746(24) = 9456942914519415532061345345175552. - Klaus Brockhaus, Apr 20 2011
%C A169040 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169040 <a href="/index/Rec#order_24">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, 25, -325).
%F A169040 G.f.: (t^24 + 2*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^24 - 25*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 A169040 With[{num=Total[2t^Range[23]]+t^24+1,den=Total[-25 t^Range[23]]+ 325t^24+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 11 2012 *)
%Y A169040 Cf. A170746 (G.f.: (1+x)/(1-26*x)).
%K A169040 nonn
%O A169040 0,2
%A A169040 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009