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%I #6 Sep 08 2022 08:45:46
%S 1,4,9,16,25,36,48,60,71,80,87,92,94,92,87,80,71,60,48,36,25,16,9,4,1,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%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);
%o Coefficients(f);
%Y Cf. A161409, A162493-A162497.
%K nonn,fini
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009
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