%N Number of reduced words of length n in the reflection group [3,4,3] of order 1152.
%C This is also the Weyl group F_4.
%D H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10.
%D J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%F G.f.: (1-x^2)*(1-x^6)*(1-x^8)*(1-x^12)/(1-x)^4
%o (Magma) G := CoxeterGroup(GrpFPCox, "F4");
%o f := GrowthFunction(G);
%Y Cf. A161409, A162493-A162497.
%A _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009