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A166610 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

%I A166610 #16 Sep 08 2022 08:45:48
%S A166610 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A166610 1262145091328,27767192009216,610878224202752,13439320932460291,
%U A166610 295665060514120836,6504631331310536193,143101889288829107868
%N A166610 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
%C A166610 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A166610 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166610 G. C. Greubel, <a href="/A166610/b166610.txt">Table of n, a(n) for n = 0..500</a>
%H A166610 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A166610 G.f.: (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)/(231*t^12 - 21*t^11 - 21*t^10 - 21*t^9 -21*t^8 -21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 -21*t + 1).
%F A166610 G.f.: (1+x)*(1-x^12)/(1 -22*x + 252*x^12 - 231*x^13). - _G. C. Greubel_, Apr 25 2019
%t A166610 coxG[{12,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 03 2015 *)
%t A166610 CoefficientList[Series[(1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13), {x, 0, 20}], x] (* _G. C. Greubel_, May 18 2016, modified Apr 25 2019 *)
%o A166610 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)) \\ _G. C. Greubel_, Apr 25 2019
%o A166610 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13) )); // _G. C. Greubel_, Apr 25 2019
%o A166610 (Sage) ((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019
%K A166610 nonn
%O A166610 0,2
%A A166610 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009