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A166439 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166439 #16 Jul 26 2024 06:01:56
%S A166439 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A166439 14367501434880,632170063134720,27815482777927680,1223881242228816930,
%U A166439 53850774658067901360,2369434084954985744190,104255099738019288455760
%N A166439 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166439 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A166439 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166439 G. C. Greubel, <a href="/A166439/b166439.txt">Table of n, a(n) for n = 0..500</a>
%H A166439 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (43,43,43,43,43,43,43,43,43,43,-946).
%F A166439 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)/(946*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
%F A166439 From _G. C. Greubel_, Jul 26 2024: (Start)
%F A166439 a(n) = 43*Sum_{j=1..10} a(n-j) - 946*a(n-11).
%F A166439 G.f.: (1+x)*(1-x^11)/(1 - 44*x + 989*x^11 - 946*x^12). (End)
%t A166439 coxG[{11,946,-43}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 08 2015 *)
%t A166439 With[{p=946, q=43}, 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 26 2024 *)
%o A166439 (Magma)
%o A166439 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166439 f:= func< p,q,x | (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12) >;
%o A166439 Coefficients(R!( f(946,43,x) )); // _G. C. Greubel_, Jul 26 2024
%o A166439 (SageMath)
%o A166439 def f(p,q,x): return (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12)
%o A166439 def A166439_list(prec):
%o A166439     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166439     return P( f(946,43,x) ).list()
%o A166439 A166439_list(30) # _G. C. Greubel_, Jul 26 2024
%Y A166439 Cf. A154638, A169452, A170764.
%K A166439 nonn
%O A166439 0,2
%A A166439 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009