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A166417 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166417 #14 Jul 25 2024 02:32:36
%S A166417 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A166417 1262145091328,27767192009216,610878224202499,13439320932449412,
%U A166417 295665060513764865,6504631331300138652,143101889288543906028
%N A166417 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166417 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A166417 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166417 G. C. Greubel, <a href="/A166417/b166417.txt">Table of n, a(n) for n = 0..500</a>
%H A166417 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (21,21,21,21,21,21,21,21,21,21,-231).
%F A166417 G.f.: (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^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 A166417 From _G. C. Greubel_, Jul 23 2024: (Start)
%F A166417 a(n) = 21*Sum_{j=1..10} a(n-j) - 231*a(n-11).
%F A166417 G.f.: (1+x)*(1 - x^11)/(1 - 22*x + 252*x^11 - 231*x^12). (End)
%t A166417 With[{p=231, q=21}, CoefficientList[Series[(1+t)*(1-t^11)/(1- (q+1)*t + (p+q)*t^11 -p*t^12), {t,0,40}], t]] (* _G. C. Greubel_, May 13 2016; Jul 23 2024 *)
%t A166417 coxG[{11, 231, -21, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 23 2024 *)
%o A166417 (Magma)
%o A166417 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166417 Coefficients(R!( (1+x)*(1-x^11)/(1-22*x+252*x^11-231*x^12) )); // _G. C. Greubel_, Jul 23 2024
%o A166417 (SageMath)
%o A166417 def A166417_list(prec):
%o A166417     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166417     return P( (1+x)*(1-x^11)/(1-22*x+252*x^11-231*x^12) ).list()
%o A166417 A166417_list(30) # _G. C. Greubel_, Jul 23 2024
%Y A166417 Cf. A154638, A169452, A170742.
%K A166417 nonn
%O A166417 0,2
%A A166417 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009