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%I #17 Sep 08 2022 08:45:46
%S 1,11,110,1045,9900,93555,884070,8353125,78924780,745717995,
%T 7045894350,66572896005,629011803420,5943197049075,56154099352230,
%U 530570136457845,5013074255082300,47365865053010955,447534797632236270
%N Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
%C The initial terms coincide with those of A003953, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H Vincenzo Librandi, <a href="/A162760/b162760.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9, 9, -45).
%F G.f.: (t^3 + 2*t^2 + 2*t + 1)/(45*t^3 - 9*t^2 - 9*t + 1).
%F G.f.: (1+x)*(1-x^3)/(1 - 10*x + 54*x^3 - 45*x^4). - _G. C. Greubel_, Apr 26 2019
%t Join[{1}, LinearRecurrence[{9, 9, -45}, {11, 110, 1045}, 19]] (* _Vincenzo Librandi_, Apr 01 2017 *)
%t CoefficientList[Series[(1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4), {x,0,20}],x] (* or *) coxG[{3, 45, -9}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 26 2019 *)
%o (Magma) I:=[1,11,110,1045]; [n le 4 select I[n] else 9*Self(n-1) +9*Self(n-2)-45*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Apr 01 2017
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4) )); // _G. C. Greubel_, Apr 26 2019
%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4)) \\ _G. C. Greubel_, Apr 26 2019
%o (Sage) ((1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 26 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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