%I #9 Nov 23 2016 22:05:52
%S 1,6,30,150,750,3750,18750,93750,468750,2343735,11718600,58592640,
%T 292961400,1464798000,7323945000,36619500000,183096375000,
%U 915476250000,4577353125210,22886625003000,114432421904040,572158593987000
%N Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
%C The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, -10).
%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 +
%F 1)/(10*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t
%F + 1)
%t With[{num=Total[2t^Range[8]]+t^9+1,den=Total[-4 t^Range[8]]+10t^9+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 22 2012 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009