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 A163803 #26 Sep 08 2022 08:45:47
%S A163803 1,47,2162,99452,4574792,210439351,9680160420,445285093005,
%T A163803 20483009107740,942213581113500,43341602191631640,1993703464046530125,
%U A163803 91709888457205975050,4218633208251709753275,194056131188825472581550
%N A163803 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163803 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A163803 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163803 Colin Barker, <a href="/A163803/b163803.txt">Table of n, a(n) for n = 0..600</a>
%H A163803 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (45,45,45,45,-1035).
%F A163803 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
%F A163803 a(n) = 45*a(n-1)+45*a(n-2)+45*a(n-3)+45*a(n-4)-1035*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%p A163803 seq(coeff(series((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6), t, n+1), t, n), n = 0 .. 20); # _G. C. Greubel_, Aug 09 2019
%t A163803 CoefficientList[Series[(1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6), {t, 0, 20}], t] (* _G. C. Greubel_, Aug 04 2017 *)
%t A163803 coxG[{5, 1035, -45}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 09 2019 *)
%o A163803 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6)) \\ _G. C. Greubel_, Aug 04 2017
%o A163803 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6) )); // _G. C. Greubel_, Aug 09 2019
%o A163803 (Sage)
%o A163803 def A163803_list(prec):
%o A163803 P.<t> = PowerSeriesRing(ZZ, prec)
%o A163803 return P((1+t)*(1-t^5)/(1-46*t+1080*t^5-1035*t^6)).list()
%o A163803 A163803_list(20) # _G. C. Greubel_, Aug 09 2019
%o A163803 (GAP) a:=[47,2162,99452,4574792,210439351];; for n in [6..30] do a[n]:=45*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -1035*a[n-5]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 09 2019
%K A163803 nonn,easy
%O A163803 0,2
%A A163803 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009