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

0,2

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.

Links

Table of n, a(n) for n=0..57.

Formula

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

Prog

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

Crossrefs

Cf. A161409, A162493-A162496.

Sequence in context: A169920 A093837 A194148 * A216500 A370785 A069821

Adjacent sequences: A162494 A162495 A162496 * A162498 A162499 A162500

Keyword

nonn,fini

Author

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

Status

approved