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 A166541 #13 Aug 23 2024 22:08:02
%S A166541 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A166541 9663676416,77309411292,618475290048,4947802318116,39582418526784,
%U A166541 316659348069120,2533274783391744,20266198257844224,162129585988435968
%N A166541 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
%C A166541 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A166541 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166541 G. C. Greubel, <a href="/A166541/b166541.txt">Table of n, a(n) for n = 0..500</a>
%H A166541 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (7,7,7,7,7,7,7,7,7,7, 7,-28).
%F A166541 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)/(28*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
%F A166541 From _G. C. Greubel_, Aug 23 2024: (Start)
%F A166541 a(n) = 7*Sum_{j=1..11} a(n-j) - 28*a(n-13).
%F A166541 G.f.: (1+x)*(1-x^12)/(1 - 8*x + 35*x^12 - 28*x^13). (End)
%t A166541 CoefficientList[Series[(1+t)*(1-t^12)/(1-8*t+35*t^12-28*t^13), {t, 0, 50}], t] (* _G. C. Greubel_, May 16 2016; Aug 23 2024 *)
%t A166541 coxG[{12,28,-7, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 23 2024 *)
%o A166541 (Magma)
%o A166541 R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^12)/(1-8*x+35*x^12-28*x^13) )); // _G. C. Greubel_, Aug 23 2024
%o A166541 (SageMath)
%o A166541 def A166541_list(prec):
%o A166541 P.<x> = PowerSeriesRing(ZZ, prec)
%o A166541 return P( (1+x)*(1-x^12)/(1-8*x+35*x^12-28*x^13) ).list()
%o A166541 A166541_list(30) # _G. C. Greubel_, Aug 23 2024
%Y A166541 Cf. A003951, A154638, A169452.
%K A166541 nonn
%O A166541 0,2
%A A166541 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009