This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A166538 #16 Aug 24 2024 02:06:07
%S A166538 1,8,56,392,2744,19208,134456,941192,6588344,46118408,322828856,
%T A166538 2259801992,15818613916,110730297216,775112079168,5425784544768,
%U A166538 37980491747520,265863441771648,1861044089174592,13027308601633536
%N A166538 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
%C A166538 The initial terms coincide with those of A003950, although the two sequences are eventually different.
%C A166538 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166538 G. C. Greubel, <a href="/A166538/b166538.txt">Table of n, a(n) for n = 0..500</a>
%H A166538 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (6,6,6,6,6,6,6,6,6,6,6,-21).
%F A166538 G.f.: (t^12 + 2*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)/(21*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).
%F A166538 From _G. C. Greubel_, Aug 23 2024: (Start)
%F A166538 a(n) = 6*Sum_{j=1..11} a(n-j) - 21*a(n-12).
%F A166538 G.f.: (1 + x)*(1 - x^12)/(1 - 7*x + 27*x^12 - 21*x^13). (End)
%t A166538 CoefficientList[Series[(1+t)*(1-t^12)/(1-7*t+27*t^12-21*t^13), {t, 0, 50}], t] (* _G. C. Greubel_, May 16 2016; Aug 23 2024 *)
%t A166538 coxG[{12,21,-6}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 24 2016 *)
%o A166538 (Magma)
%o A166538 R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^12)/(1-7*x+27*x^12-21*x^13) )); // _G. C. Greubel_, Aug 23 2024
%o A166538 (SageMath)
%o A166538 def A166538_list(prec):
%o A166538 P.<x> = PowerSeriesRing(ZZ, prec)
%o A166538 return P( (1+x)*(1-x^12)/(1-7*x+27*x^12-21*x^13) ).list()
%o A166538 A166538_list(30) # _G. C. Greubel_, Aug 23 2024
%Y A166538 Cf. A003950, A154638, A169452.
%K A166538 nonn
%O A166538 0,2
%A A166538 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009