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

0,2

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.

Links

Table of n, a(n) for n=0..95.

Formula

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

Prog

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

Crossrefs

Cf. A161409, A162493-A162497.

Sequence in context: A241971 A335640 A302053 * A159852 A343066 A028907

Adjacent sequences: A162493 A162494 A162495 * A162497 A162498 A162499

Keyword

nonn,fini

Author

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

Status

approved