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%I #24 Sep 08 2022 08:45:46
%S 1,41,1640,65600,2623180,104894400,4194464820,167726145600,
%T 6706948607580,268194081870000,10724409825744420,428842296999090000,
%U 17148329715447559980,685718769084764781600,27420176663127165184020
%N Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C The initial terms coincide with those of A170760, 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="/A163224/b163224.txt">Table of n, a(n) for n = 0..620</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (39,39,39,-780).
%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
%F a(n) = 39*a(n-1)+39*a(n-2)+39*a(n-3)-780*a(n-4). - _Wesley Ivan Hurt_, May 06 2021
%t CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3-39*t^2 - 39*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {39, 39, 39, -780}, {41,1640,65600,2623180} 20]] (* _G. C. Greubel_, Dec 11 2016 *)
%t coxG[{4,780,-39}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 18 2019 *)
%o (PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3- 39*t^2-39*t+1)) \\ _G. C. Greubel_, Dec 11 2016
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-40*x+819*x^4-780*x^5) )); // _G. C. Greubel_, Apr 30 2019
%o (Sage) ((1+x)*(1-x^4)/(1-40*x+819*x^4-780*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
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