A162496 Number of reduced words of length n in the reflection group [3,4,3] of order 1152.

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, 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, 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

Offset: 0

Author

John Cannon and N. J. A. Sloane, Dec 01 2009

Keywords

• nonn
• fini

Comments

This is also the Weyl group F_4.

References

• H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10.
• J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.

Crossrefs

Cf. A161409, A162493-A162497.

Programs

Magma

G := CoxeterGroup(GrpFPCox, "F4");
f := GrowthFunction(G);
Coefficients(f);

Formula

G.f.: (1-x^2)*(1-x^6)*(1-x^8)*(1-x^12)/(1-x)^4