A162496 - OEIS

%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