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%I #16 Sep 08 2022 08:45:46
%S 1,44,1892,81356,3497362,150345888,6463124976,277839201024,
%T 11943854101410,513446807614356,22072240836651852,948849634132915284,
%U 40789498214388049434,1753474001285744132472,75378987430163637459624
%N Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C The initial terms coincide with those of A170763, 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="/A163230/b163230.txt">Table of n, a(n) for n = 0..600</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, -903).
%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
%F a(n) = 42*a(n-1)+42*a(n-2)+42*a(n-3)-903*a(n-4). - _Wesley Ivan Hurt_, May 06 2021
%t coxG[{4,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 18 2015 *)
%t CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3-42*t^2 - 42*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {42, 42, 42, -903}, {44,1892,81356,3497362}, 50]] (* _G. C. Greubel_, Dec 11 2016 *)
%o (PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3 - 42*t^2-42*t+1)) \\ _G. C. Greubel_, Dec 11 2016
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-43*x+945*x^4-903*x^5) )); // _G. C. Greubel_, Apr 30 2019
%o (Sage) ((1+x)*(1-x^4)/(1-43*x+945*x^4-903*x^5)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 30 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009