%I #18 Sep 08 2022 08:45:46
%S 1,4,12,36,108,318,936,2760,8136,23976,70662,208260,613788,1808964,
%T 5331420,15712878,46309320,136483800,402247944,1185513624,3493970742,
%U 10297504260,30349021740,89445276900,263615006412,776931706398
%N Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C The initial terms coincide with those of A003946, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A163315/b163315.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2, 2, 2, 2, -3).
%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1).
%F a(n) = 2*a(n-1)+2*a(n-2)+2*a(n-3)+2*a(n-4)-3*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t CoefficientList[Series[(1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6), {x,0,30}], x] (* or *) Join[{1}, LinearRecurrence[{2,2,2,2,-3}, {1,4,12,36,108,318}, 30]] (* _G. C. Greubel_, Dec 18 2016 *)
%t coxG[{4, 3, -2}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 12 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6)) \\ _G. C. Greubel_, Dec 18 2016
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6) )); // _G. C. Greubel_, May 12 2019
%o (Sage) ((1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 12 2019
%K nonn,easy
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009