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 A163207 #15 Sep 08 2022 08:45:46
%S A163207 1,29,812,22736,636202,17802288,498146166,13939191504,390048294510,
%T A163207 10914382803996,305407698579522,8545958486918244,239134137088822794,
%U A163207 6691482951706744632,187241958166564053774,5239429159586654676168
%N A163207 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A163207 The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C A163207 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163207 G. C. Greubel, <a href="/A163207/b163207.txt">Table of n, a(n) for n = 0..685</a>
%H A163207 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, -378).
%F A163207 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
%F A163207 From _G. C. Greubel_, Apr 28 2019: (Start)
%F A163207 a(n) = 27*(a(n-1) + a(n-2) + a(n-3) -14*a(n-4)).
%F A163207 G.f.: (1+x)*(1-x^4)/(1 - 28*x + 405*x^4 - 378*x^5). (End)
%t A163207 CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(378*t^4-27*t^3-27*t^2 - 27*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{27,27,27,-378}, {1,29, 812,22736,636202}, 20] (* _G. C. Greubel_, Dec 10 2016 *)
%t A163207 coxG[{4, 378, -27}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 28 2019 *)
%o A163207 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5)) \\ _G. C. Greubel_, Dec 10 2016, modified Apr 28 2019
%o A163207 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5) )); // _G. C. Greubel_, Apr 28 2019
%o A163207 (Sage) ((1+x)*(1-x^4)/(1-28*x+405*x^4-378*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019
%o A163207 (GAP) a:=[29,812,22736,636202];; for n in [5..20] do a[n]:=27*(a[n-1] +a[n-2]+a[n-3] -14*a[n-4]); od; Concatenation([1], a); # _G. C. Greubel_, Apr 28 2019
%K A163207 nonn,easy
%O A163207 0,2
%A A163207 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009