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 A163208 #15 Sep 08 2022 08:45:46
%S A163208 1,30,870,25230,731235,21193200,614237400,17802288000,515959239390,
%T A163208 14953916974920,433405617680280,12561286100120520,364060598322527820,
%U A163208 10551476830837383840,305810801346502707360,8863237603561904401440
%N A163208 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A163208 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A163208 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163208 G. C. Greubel, <a href="/A163208/b163208.txt">Table of n, a(n) for n = 0..680</a>
%H A163208 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, -406).
%F A163208 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(406*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
%F A163208 From _G. C. Greubel_, Apr 28 2019: (Start)
%F A163208 a(n) = 28*(a(n-1) + a(n-2) + a(n-3)) - 406*a(n-4).
%F A163208 G.f.: (1+x)*(1-x^4)/(1 - 29*x + 434*x^4 - 406*x^5). (End)
%t A163208 CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(406*t^4-28*t^3-28*t^2- 28*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{28,28,28,-406}, {1,30, 870,25230,731235}, 20] (* _G. C. Greubel_, Dec 10 2016 *)
%t A163208 coxG[{4, 406, -28}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 28 2019 *)
%o A163208 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-29*x+434*x^4-406*x^5)) \\ _G. C. Greubel_, Dec 10 2016, modified Apr 28 2019
%o A163208 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-29*x+434*x^4-406*x^5) )); // _G. C. Greubel_, Apr 28 2019
%o A163208 (Sage) ((1+x)*(1-x^4)/(1-29*x+434*x^4-406*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019
%o A163208 (GAP) a:=[30,870,25230,731235];; for n in [5..20] do a[n]:=28*(a[n-1] + a[n-2]+a[n-3]) -406*a[n-4]; od; Concatenation([1], a); # _G. C. Greubel_, Apr 28 2019
%K A163208 nonn,easy
%O A163208 0,2
%A A163208 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009