%I #8 Nov 23 2016 15:23:30
%S 1,16,240,3480,50400,729120,10547880,152586000,2207316720,31931110680,
%T 461916453600,6682097644320,96663430749480,1398336169885200,
%U 20228374156231920,292624284336944280,4233111921066520800
%N Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
%C The initial terms coincide with those of A170735, 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 (14, 14, -105).
%F G.f.: (t^3 + 2*t^2 + 2*t + 1)/(105*t^3 - 14*t^2 - 14*t + 1)
%t CoefficientList[Series[(t^3+2t^2+2t+1)/(105t^3-14t^2-14t+1), {t,0,30}],t] (* _Harvey P. Dale_, Oct 02 2011 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009