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A166424 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166424 #16 Jul 25 2024 14:48:01
%S A166424 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T A166424 15007392388830,435214379276070,12621216999005595,366015292971149640,
%U A166424 10614443496162974160,307818861388715654040,8926746980272446665760
%N A166424 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166424 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A166424 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166424 G. C. Greubel, <a href="/A166424/b166424.txt">Table of n, a(n) for n = 0..500</a>
%H A166424 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (28,28,28,28,28,28,28,28,28,28,-406).
%F A166424 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)/(406*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
%F A166424 From _G. C. Greubel_, Jul 25 2024: (Start)
%F A166424 a(n) = 28*Sum_{j=1..10} a(n-j) - 406*a(n-11).
%F A166424 G.f.: (1+x)*(1-x^11)/(1 - 29*x + 434*x^11 - 406*x^12). (End)
%t A166424 With[{p=406, q=28}, 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 A166424 coxG[{11,406,-28}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 12 2016 *)
%o A166424 (Magma)
%o A166424 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166424 Coefficients(R!( (1+x)*(1-x^11)/(1-29*x+434*x^11-406*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166424 (SageMath)
%o A166424 def A166424_list(prec):
%o A166424     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166424     return P( (1+x)*(1-x^11)/(1-29*x+434*x^11-406*x^12) ).list()
%o A166424 A166424_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166424 Cf. A154638, A169452, A170749.
%K A166424 nonn
%O A166424 0,2
%A A166424 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009