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A163743 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163743 #15 Sep 08 2022 08:45:47
%S A163743 1,42,1722,70602,2894682,118681101,4865889840,199500036960,
%T A163743 8179442209680,335354699064000,13749442969516380,563723074403412000,
%U A163743 23112478470537775200,947604746561778765600,38851512911134346287200
%N A163743 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163743 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A163743 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163743 G. C. Greubel, <a href="/A163743/b163743.txt">Table of n, a(n) for n = 0..615</a>
%H A163743 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, -820).
%F A163743 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*t^5 - 40*t^4 - 40*t^3 - 40*t^2- 40*t + 1).
%F A163743 a(n) = 40*a(n-1)+40*a(n-2)+40*a(n-3)+40*a(n-4)-820*a(n-5). - _Wesley Ivan Hurt_, May 11 2021
%t A163743 CoefficientList[Series[(1+x)*(1-x^5)/(1-41*x+860*x^5-820*x^6), {x,0,20}], x] (* _G. C. Greubel_, Aug 02 2017 *)
%t A163743 coxG[{5, 820, -40}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 24 2019 *)
%o A163743 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-41*x+860*x^5-820*x^6)) \\ _G. C. Greubel_, Aug 02 2017
%o A163743 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-41*x+860*x^5-820*x^6) )); // _G. C. Greubel_, May 24 2019
%o A163743 (Sage) ((1+x)*(1-x^5)/(1-41*x+860*x^5-820*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 24 2019
%K A163743 nonn
%O A163743 0,2
%A A163743 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009