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A162497 Number of reduced words of length n in the reflection group [3,3,5] of order 14400. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A069821 A331221

Adjacent sequences: A162494 A162495 A162496 * A162498 A162499 A162500

KEYWORD

nonn,fini

AUTHOR

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

STATUS

approved

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Last modified January 31 05:03 EST 2023. Contains 359947 sequences. (Running on oeis4.)