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%I #5 Nov 23 2016 15:24:32
%S 1,18,306,5049,83232,1370880,22579128,371880576,6124915584,
%T 100877977152,1661470525440,27364587522048,450697523867136,
%U 7423033790767104,122258117131149312,2013603551504732160,33164254102629777408
%N Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
%C The initial terms coincide with those of A170737, 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_03">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, -136).
%F G.f.: (t^3 + 2*t^2 + 2*t + 1)/(136*t^3 - 16*t^2 - 16*t + 1)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009