%I #18 Dec 03 2025 17:11:30

%S 1,20,380,7220,137180,2606230,49514760,940712040,17872229160,

%T 339547661640,6450936451470,122558879953620,2328449391567180,

%U 44237321450224020,840447989197392780,15967350630411275430

%N Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%C The initial terms coincide with those of A170739, 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="/A163454/b163454.txt">Table of n, a(n) for n = 0..750</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (18, 18, 18, 18, -171).

%F G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

%F a(n) = 18*a(n-1)+18*a(n-2)+18*a(n-3)+18*a(n-4)-171*a(n-5). - _Wesley Ivan Hurt_, May 10 2021

%t CoefficientList[Series[(1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{18, 18, 18, 18, -171}, {1, 20, 380, 7220, 137180, 2606230}, 20] (* _G. C. Greubel_, Dec 24 2016 *)

%t coxG[{5, 171, -18}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 13 2019 *)

%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6)) \\ _G. C. Greubel_, Dec 24 2016

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6) )); // _G. C. Greubel_, May 13 2019

%o (SageMath) ((1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 13 2019

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009