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A166430 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166430 #13 Jul 25 2024 23:05:45
%S A166430 1,36,1260,44100,1543500,54022500,1890787500,66177562500,
%T A166430 2316214687500,81067514062500,2837362992187500,99307704726561870,
%U A166430 3475769665429643400,121651938290036747880,4257817840151259186600,149023624405293126909000
%N A166430 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166430 The initial terms coincide with those of A170755, although the two sequences are eventually different.
%C A166430 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166430 G. C. Greubel, <a href="/A166430/b166430.txt">Table of n, a(n) for n = 0..500</a>
%H A166430 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (34,34,34,34,34,34,34,34,34,34,-595).
%F A166430 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)/(595*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
%F A166430 From _G. C. Greubel_, Jul 25 2024: (Start)
%F A166430 a(n) = 34*Sum_{j=1..10} a(n-j) - 595*a(n-11).
%F A166430 G.f.: (1+x)*(1-x^11)/(1 - 35*x + 629*x^11 - 595*x^12). (End)
%t A166430 With[{p=595, q=34}, 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 14 2016; Jul 25 2024 *)
%t A166430 coxG[{11, 595, -34, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 25 2024 *)
%o A166430 (Magma)
%o A166430 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166430 Coefficients(R!( (1+x)*(1-x^11)/(1-35*x+629*x^11-595*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166430 (SageMath)
%o A166430 def A166430_list(prec):
%o A166430     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166430     return P( (1+x)*(1-x^11)/(1-35*x+629*x^11-595*x^12) ).list()
%o A166430 A166430_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166430 Cf. A154638, A169452, A170755.
%K A166430 nonn
%O A166430 0,2
%A A166430 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009