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A166418 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166418 #13 Jul 24 2024 08:59:18
%S A166418 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A166418 1879463646744,43227663875112,994236269127300,22867434189921552,
%U A166418 525950986368049968,12096872686461797520,278228071788544252848
%N A166418 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166418 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A166418 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166418 G. C. Greubel, <a href="/A166418/b166418.txt">Table of n, a(n) for n = 0..500</a>
%H A166418 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (22,22,22,22,22,22,22,22,22,22,-253).
%F A166418 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)/(253*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
%F A166418 From _G. C. Greubel_, Jul 23 2024: (Start)
%F A166418 a(n) = 22*Sum_{j=1..10} a(n-j) - 253*a(n-11).
%F A166418 G.f.: (1+x)*(1 - x^11)/(1 - 23*x + 275*x^11 - 253*x^12). (End)
%t A166418 With[{p=253, q=22}, 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 A166418 coxG[{11, 253, -22, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 23 2024 *)
%o A166418 (Magma)
%o A166418 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166418 Coefficients(R!( (1+x)*(1-x^11)/(1-23*x+275*x^11-253*x^12) )); // _G. C. Greubel_, Jul 23 2024
%o A166418 (SageMath)
%o A166418 def A166418_list(prec):
%o A166418     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166418     return P( (1+x)*(1-x^11)/(1-23*x+275*x^11-253*x^12) ).list()
%o A166418 A166418_list(30) # _G. C. Greubel_, Jul 23 2024
%Y A166418 Cf. A154638, A169452, A170743.
%K A166418 nonn
%O A166418 0,2
%A A166418 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009