A162497 Number of reduced words of length n in the reflection group [3,3,5] of order 14400.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 168, 192, 216, 240, 264, 288, 312, 336, 359, 380, 399, 416, 431, 444, 455, 464, 471, 476, 478, 476, 471, 464, 455, 444, 431, 416, 399, 380, 359, 336, 312, 288, 264, 240, 216, 192, 168, 144, 121, 100, 81, 64, 49, 36, 25, 16

Offset: 0

Author

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

Keywords

• nonn
• fini

Comments

This is also the Weyl group H_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-A162496.

Programs

Magma

G := CoxeterGroup(GrpFPCox, "H4");
f := GrowthFunction(G);
Coefficients(f);

Formula

G.f.: (1-x^2)*(1-x^12)*(1-x^20)*(1-x^30)/(1-x)^4.