A165692 - OEIS

%I #9 Nov 23 2016 22:17:03

%S 1,41,1640,65600,2624000,104960000,4198400000,167936000000,

%T 6717440000000,268697599999180,10747903999934400,429916159996064820,

%U 17196646399790145600,687865855989507936000,27514634239496401920000

%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)^9 = 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 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, -780).

%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)/(780*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 -

%F 39*t^2 - 39*t + 1)

%t With[{num=Total[2t^Range[8]]+t^9+1,den=Total[-39 t^Range[8]]+ 780t^9+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 20 2011 *)

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009