A165699 - OEIS

%I #11 Sep 08 2022 08:45:48

%S 1,45,1980,87120,3833280,168664320,7421230080,326534123520,

%T 14367501434880,632170063133730,27815482777840560,1223881242223068990,

%U 53850774657730746960,2369434084936444167840,104255099737040360655360

%N Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

%C The initial terms coincide with those of A170764, 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="/A165699/b165699.txt">Table of n, a(n) for n = 0..600</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, -946).

%F G.f.: (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).

%F G.f.: (1+x)*(1-x^9)/(1 -44*x +989*x^9 -946*x^10). - _G. C. Greubel_, Apr 26 2019

%t CoefficientList[Series[(1+x)*(1-x^9)/(1-44*x+989*x^9-946*x^10), {x, 0, 20}], x] (* or *) coxG[{9, 946, -43}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 26 2019 *)

%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^9)/(1-44*x+989*x^9-946*x^10)) \\ _G. C. Greubel_, Apr 26 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^9)/(1-44*x+989*x^9-946*x^10) )); // _G. C. Greubel_, Apr 26 2019

%o (Sage) ((1+x)*(1-x^9)/(1-44*x+989*x^9-946*x^10)).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