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A164696 Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I. 0

%I

%S 1,3,6,12,24,48,96,192,381,756,1503,2988,5940,11808,23472,46656,92742,

%T 184353,366456,728439,1447986,2878296,5721456,11373072,22607316,

%U 44938668,89328777,177567132,352966731,701624856,1394685096,2772345504

%N Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

%C The initial terms coincide with those of A003945, 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 (1, 1, 1, 1, 1, 1, 1, -1).

%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)/(t^8 - t^7 -

%F t^6 - t^5 - t^4 - t^3 - t^2 - t + 1)

%t With[{num=Total[2t^Range[7]]+t^8+1,den=Total[-t^Range[7]]+t^8+1},CoefficientList[ Series[ num/den,{t,0,40}],t]] (* _Harvey P. Dale_, Aug 05 2011 *)

%K nonn

%O 0,2

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

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)