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 A166518 #14 Aug 03 2024 02:31:53
%S A166518 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,
%T A166518 423263232,2539579371,15237476100,91424855865,548549130780,
%U A166518 3291294758220,19747768390560,118486609390800,710919650629440,4265517869484480
%N A166518 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
%C A166518 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A166518 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166518 G. C. Greubel, <a href="/A166518/b166518.txt">Table of n, a(n) for n = 0..500</a>
%H A166518 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (5,5,5,5,5,5,5,5,5,5,5,-15).
%F A166518 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)/(15*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
%F A166518 From _G. C. Greubel_, Aug 03 2024: (Start)
%F A166518 a(n) = 5*Sum_{j=1..11} a(n-j) - 15*a(n-12).
%F A166518 G.f.: (1+x)*(1-x^12)/(1 - 6*x + 20*x^12 - 15*x^13). (End)
%t A166518 With[{p=15, q=5}, CoefficientList[Series[(1+t)*(1-t^12)/(1 - (q+1)*t + (p+q)*t^12 - p*t^13), {t,0,40}], t]] (* _G. C. Greubel_, May 15 2016; Aug 03 2024 *)
%t A166518 coxG[{12, 15, -5, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 03 2024 *)
%o A166518 (PARI) Vec((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)/(15*t^12 - 5*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1)+O(t^99))
%o A166518 (Magma)
%o A166518 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166518 f:= func< p,q,x | (1+x)*(1-x^12)/(1-(q+1)*x+(p+q)*x^12-p*x^13) >;
%o A166518 Coefficients(R!( f(15,5,x) )); // _G. C. Greubel_, Aug 03 2024
%o A166518 (SageMath)
%o A166518 def f(p,q,x): return (1+x)*(1-x^12)/(1-(q+1)*x+(p+q)*x^12-p*x^13)
%o A166518 def A166518_list(prec):
%o A166518 P.<x> = PowerSeriesRing(ZZ, prec)
%o A166518 return P( f(15,5,x) ).list()
%o A166518 A166518_list(30) # _G. C. Greubel_, Aug 03 2024
%Y A166518 Cf. A003949, A154638, A169452.
%K A166518 nonn,easy
%O A166518 0,2
%A A166518 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009