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A163503 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163503 #21 Sep 08 2022 08:45:46
%S A163503 1,21,420,8400,168000,3359790,67191600,1343748210,26873288400,
%T A163503 537432252000,10747974763890,214946090593500,4298653734898110,
%U A163503 85967713492846500,1719247052441058000,34382796834223386990
%N A163503 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163503 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A163503 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163503 G. C. Greubel, <a href="/A163503/b163503.txt">Table of n, a(n) for n = 0..765</a>
%H A163503 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, -190).
%F A163503 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).
%F A163503 a(n) = 19*a(n-1)+19*a(n-2)+19*a(n-3)+19*a(n-4)-190*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163503 coxG[{5,190,-19}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 09 2015 *)
%t A163503 CoefficientList[Series[(1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6), {x,0,20}], x] (* _G. C. Greubel_, Jul 26 2017 *)
%o A163503 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6)) \\ _G. C. Greubel_, Jul 26 2017
%o A163503 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6) )); // _G. C. Greubel_, May 16 2019
%o A163503 (Sage) ((1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 16 2019
%K A163503 nonn
%O A163503 0,2
%A A163503 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009