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A166425 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166425 #16 Jul 25 2024 20:59:38
%S A166425 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A166425 20339100000000,610173000000000,18305189999999535,549155699999972100,
%U A166425 16474670999998744965,494240129999949807900,14827203899998118005500
%N A166425 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166425 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A166425 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166425 G. C. Greubel, <a href="/A166425/b166425.txt">Table of n, a(n) for n = 0..500</a>
%H A166425 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (29,29,29,29,29,29,29,29,29,29,-435).
%F A166425 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)/(435*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
%F A166425 From _G. C. Greubel_, Jul 25 2024: (Start)
%F A166425 a(n) = 29*Sum_{j=1..10} a(n-j) - 435*a(n-11).
%F A166425 G.f.: (1+x)*(1-x^11)/(1 - 30*x + 464*x^11 - 435*x^12). (End)
%t A166425 With[{p=435, q=29}, 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 25 2024 *)
%t A166425 coxG[{11,435,-29}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 26 2021 *)
%o A166425 (Magma)
%o A166425 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166425 Coefficients(R!( (1+x)*(1-x^11)/(1-30*x+464*x^11-435*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166425 (SageMath)
%o A166425 def A166425_list(prec):
%o A166425     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166425     return P( (1+x)*(1-x^11)/(1-30*x+464*x^11-435*x^12) ).list()
%o A166425 A166425_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166425 Cf. A154638, A169452, A170750.
%K A166425 nonn
%O A166425 0,2
%A A166425 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009