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Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.
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%I #13 Feb 23 2024 04:20:47

%S 1,6,30,150,750,3750,18750,93750,468735,2343600,11717640,58586400,

%T 292923000,1464570000,7322625000,36612000000,183054375210,

%U 915243753000,4576078154040,22879687737000,114394923627000,571957043385000

%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)^8 = 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_08">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, -10).

%F G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).

%t With[{num=Total[2t^Range[7]]+t^8+1, den=Total[-4 t^Range[7]]+10t^8+1}, CoefficientList[Series[num/den,{t,0,25}],t]] (* _Harvey P. Dale_, Jul 14 2011 *)

%K nonn

%O 0,2

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