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A166426 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166426 #16 Jul 25 2024 23:05:18
%S A166426 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A166426 27292513198112,846067909141472,26228105183385136,813071260684923840,
%U A166426 25205209081232162880,781361481518182288320,24222205927063193348160
%N A166426 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166426 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A166426 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166426 G. C. Greubel, <a href="/A166426/b166426.txt">Table of n, a(n) for n = 0..500</a>
%H A166426 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (30,30,30,30,30,30,30,30,30,30,-465).
%F A166426 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)/(465*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
%F A166426 From _G. C. Greubel_, Jul 25 2024: (Start)
%F A166426 a(n) = 30*Sum_{j=1..10} a(n-j) - 465*a(n-11).
%F A166426 G.f.: (1+x)*(1-x^11)/(1 - 31*x + 495*x^11 - 465*x^12). (End)
%t A166426 coxG[{11,465,-30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 06 2015 *)
%t A166426 With[{p=465, q=30}, 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 *)
%o A166426 (Magma)
%o A166426 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166426 Coefficients(R!( (1+x)*(1-x^11)/(1-31*x+495*x^11-465*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166426 (SageMath)
%o A166426 def A166426_list(prec):
%o A166426     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166426     return P( (1+x)*(1-x^11)/(1-31*x+495*x^11-465*x^12) ).list()
%o A166426 A166426_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166426 Cf. A154638, A169452, A170751.
%K A166426 nonn
%O A166426 0,2
%A A166426 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009