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A166433 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166433 #15 Jul 25 2024 23:06:08
%S A166433 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A166433 4462207721088,169563893401344,6443427949251072,244850262071539995,
%U A166433 9304309958718491652,353563778431301613513,13435423580389420681500
%N A166433 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166433 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A166433 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166433 G. C. Greubel, <a href="/A166433/b166433.txt">Table of n, a(n) for n = 0..500</a>
%H A166433 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (37,37,37,37,37,37,37,37,37,37,-703).
%F A166433 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)/(703*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
%F A166433 From _G. C. Greubel_, Jul 25 2024: (Start)
%F A166433 a(n) = 37*Sum_{j=1..10} a(n-j) - 703*a(n-11).
%F A166433 G.f.: (1+x)*(1-x^11)/(1 - 38*x + 740*x^11 - 703*x^12). (End)
%t A166433 With[{p=703, q=37}, 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 A166433 coxG[{11,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 06 2019 *)
%o A166433 (Magma)
%o A166433 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166433 Coefficients(R!( (1+x)*(1-x^11)/(1-38*x+740*x^11-703*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166433 (SageMath)
%o A166433 def A166423_list(prec):
%o A166433     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166433     return P( (1+x)*(1-x^11)/(1-38*x+740*x^11-703*x^12) ).list()
%o A166433 A166423_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166433 Cf. A154638, A169452, A170758.
%K A166433 nonn
%O A166433 0,2
%A A166433 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009