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 A163221 #21 Sep 08 2022 08:45:46
%S A163221 1,38,1406,52022,1924111,71166096,2632183848,97355219328,
%T A163221 3600827035866,133181923185576,4925930761424952,182192847843197736,
%U A163221 6738672428195210748,249239784283952410080,9218502714272560450272
%N A163221 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A163221 The initial terms coincide with those of A170757, although the two sequences are eventually different.
%C A163221 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163221 G. C. Greubel, <a href="/A163221/b163221.txt">Table of n, a(n) for n = 0..635</a>
%H A163221 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (36, 36, 36, -666).
%F A163221 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).
%F A163221 a(n) = 36*a(n-1)+36*a(n-2)+36*a(n-3)-666*a(n-4). - _Wesley Ivan Hurt_, May 06 2021
%t A163221 coxG[{4,666,-36}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 09 2015 *)
%t A163221 CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(666*t^4-36*t^3-36*t^2 - 36*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{36, 36, 36, -666}, {1, 38, 1406, 52022, 1924111}, 20] (* _G. C. Greubel_, Dec 11 2016; modified by _Georg Fischer_, Apr 08 2019 *)
%o A163221 (PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(666*t^4-36*t^3 - 36*t^2-36*t+1)) \\ _G. C. Greubel_, Dec 11 2016
%o A163221 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-37*x+702*x^4-666*x^5) )); // _G. C. Greubel_, May 01 2019
%o A163221 (Sage) ((1+x)*(1-x^4)/(1-37*x+702*x^4-666*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 01 2019
%o A163221 (GAP) a:=[38,1406,52022,1924111];; for n in [5..20] do a[n]:=36*(a[n-1]+ a[n-2]+a[n-3]) -666*a[n-4]; od; Concatenation([1], a); # _G. C. Greubel_, May 01 2019
%K A163221 nonn
%O A163221 0,2
%A A163221 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009