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 A166599 #13 Dec 08 2024 03:59:43
%S A166599 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A166599 125563633938,2134581776946,36287890208082,616894133537241,
%U A166599 10487200270130496,178282404592174368,3030800878066215168,51523614927112923360
%N A166599 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
%C A166599 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A166599 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166599 G. C. Greubel, <a href="/A166599/b166599.txt">Table of n, a(n) for n = 0..500</a>
%H A166599 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (16,16,16,16,16,16,16,16,16,16,16,-136).
%F A166599 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)/(136*t^12 - 16*t^11 - 16*t^10 - 16*t^9 -16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 -16*t +1).
%F A166599 From _G. C. Greubel_, Dec 08 2024: (Start)
%F A166599 a(n) = 16*Sum_{j=1..11} a(n-j) - 136*a(n-12).
%F A166599 G.f.: (1+x)*(1-x^12)/(1 - 17*x + 152*x^12 - 136*x^13). (End)
%t A166599 CoefficientList[Series[(1+t)*(1-t^12)/(1-17*t+152*t^12-136*t^13), {t,0,50}], t] (* _G. C. Greubel_, May 18 2016; Dec 08 2024 *)
%t A166599 coxG[{12,136,-16,40}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Dec 08 2024 *)
%o A166599 (Magma)
%o A166599 R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^12)/(1 - 17*x+152*x^12-136*x^13) )); // _G. C. Greubel_, Dec 08 2024
%o A166599 (SageMath)
%o A166599 def A166599_list(prec):
%o A166599 P.<x> = PowerSeriesRing(ZZ, prec)
%o A166599 return P( (1+x)*(1-x^12)/(1-17*x+152*x^12-136*x^13) ).list()
%o A166599 print(A166599_list(40)) # _G. C. Greubel_, Dec 08 2024
%Y A166599 Cf. A154638, A169452, A170737.
%K A166599 nonn
%O A166599 0,2
%A A166599 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009