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A162496 Number of reduced words of length n in the reflection group [3,4,3] of order 1152. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)