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A169468 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%I A169468 #11 Feb 14 2025 19:33:45
%S A169468 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A169468 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A169468 295665060514131968,6504631331310903296,143101889288839872512
%N A169468 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
%C A169468 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A169468 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169468 <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A169468 G.f. (t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A169468 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A169468 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A169468 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 +
%F A169468 1)/(231*t^33 - 21*t^32 - 21*t^31 - 21*t^30 - 21*t^29 - 21*t^28 - 21*t^27
%F A169468 - 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 -
%F A169468 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 -
%F A169468 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5
%F A169468 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1)
%t A169468 With[{num=Total[2t^Range[32]]+t^33+1,den=Total[-21 t^Range[32]]+ 231t^33+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Sep 16 2011 *)
%t A169468 coxG[{33,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 14 2025 *)
%K A169468 nonn
%O A169468 0,2
%A A169468 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009