|
%I #19 Sep 08 2022 08:45:46
%S 1,36,1260,44100,1543500,54021870,1890743400,66175247880,
%T 2316106686600,81062789409000,2837164567941270,99299602743358500,
%U 3475445596778953980,121639178430430006500,4257321634653990493500,149004520868736130568670
%N Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C The initial terms coincide with those of A170755, 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="/A163601/b163601.txt">Table of n, a(n) for n = 0..645</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (34, 34, 34, 34, -595).
%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(595*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
%F a(n) = 34*a(n-1)+34*a(n-2)+34*a(n-3)+34*a(n-4)-595*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t CoefficientList[Series[(1+x)*(1-x^5)/(1-35*x+629*x^5-595*x^6), {x, 0, 20}], x] (* _G. C. Greubel_, Jul 29 2017 *)
%t coxG[{5, 595, -34}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 22 2019 *)
%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-35*x+629*x^5-595*x^6)) \\ _G. C. Greubel_, Jul 29 2017
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-35*x+629*x^5-595*x^6) )); // _G. C. Greubel_, May 22 2019
%o (Sage) ((1+x)*(1-x^4)/(1-35*x+629*x^5-595*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 22 2019
%o (GAP) a:=[36, 1260, 44100, 1543500, 54021870];; for n in [6..20] do a[n]:=34*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) - 595*a[n-5]; od; Concatenation([1], a); # _G. C. Greubel_, May 22 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
| 