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A169424 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169424 #14 May 08 2018 01:01:00
%S A169424 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A169424 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A169424 2576581829865418752,66991127576500887552,1741769316989023076352
%N A169424 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169424 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A169424 First disagreement is at index 32, the difference is 351. - _Klaus Brockhaus_, Jun 27 2011
%C A169424 Computed with Magma using commands similar to those used to compute A154638.
%H A169424 <a href="/index/Rec#order_32">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, 25, 25, 25, 25, 25, 25, 25, 25, -325).
%F A169424 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*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^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*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 -
%F A169424   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).
%F A169424 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-25*sum(k=1..31, x^k)+325*x^32).
%t A169424 With[{num=Total[2t^Range[31]]+t^32+1,den=Total[-25 t^Range[31]]+ 325t^32+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]]  (* _Harvey P. Dale_, Jun 18 2012 *)
%Y A169424 Cf. A170746 (G.f.: (1+x)/(1-26*x) ).
%K A169424 nonn
%O A169424 0,2
%A A169424 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009