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 A162983 #12 Apr 25 2024 09:19:53
%S A162983 1,10,90,810,7245,64800,579600,5184000,46366380,414707040,3709193760,
%T A162983 33175513440,296726124240,2653957198080,23737339710720,
%U A162983 212309865780480,1898927161041600,16984252473131520,151909371770042880
%N A162983 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A162983 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A162983 Computed with MAGMA using commands similar to those used to compute A154638.
%H A162983 G. C. Greubel, <a href="/A162983/b162983.txt">Table of n, a(n) for n = 0..1000</a>
%H A162983 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8, 8, 8, -36).
%F A162983 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
%F A162983 From _G. C. Greubel_, Apr 28 2019: (Start)
%F A162983 a(n) = 8*(a(n-1) + a(n-2) + a(n-3)) - 36*a(n-4).
%F A162983 G.f.: (1+x)*(1-x^4)/(1 - 9*x + 44*x^4 - 36*x^5). (End)
%t A162983 CoefficientList[Series[(1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5), {x,0,20}], x]
%t A162983 (* or *) coxG[{4, 36, -8}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 28 2019 *)
%o A162983 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5)) \\ _G. C. Greubel_, Apr 28 2019
%o A162983 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5) )); // _G. C. Greubel_, Apr 28 2019
%o A162983 (Sage) ((1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019
%o A162983 (GAP) a:=[10,90,810,7245];; for n in [5..20] do a[n]:=8*(a[n-1]+a[n-2] +a[n-3]) - 36*a[n-4]; od; Concatenation([1], a); # _G. C. Greubel_, Apr 28 2019
%K A162983 nonn
%O A162983 0,2
%A A162983 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009