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A266784 The growth series for the affine Weyl group F_4. 0
1, 5, 14, 30, 55, 92, 144, 214, 305, 419, 559, 729, 933, 1173, 1451, 1771, 2137, 2552, 3018, 3537, 4111, 4744, 5441, 6205, 7037, 7940, 8919, 9977, 11116, 12338, 13646, 15043, 16533, 18120, 19805, 21590, 23480, 25480, 27592, 29817, 32158, 34618, 37200, 39908, 42745, 45713, 48815, 52056, 55439, 58965, 62637, 66459, 70434, 74564, 78852, 83301 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

N. Bourbaki, Groups et Algèbres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10b, page 231, W_a(t).

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; also Table 3.1 page 59.

LINKS

Table of n, a(n) for n=0..55.

FORMULA

G.f. = (1+t)*(1+t+t^2+t^3+t^4+t^5)*(1+t+t^2+t^3+t^4+t^5+t^6+t^7)* (1+t+t^2+t^3+t^4+t^5+t^6+t^7+t^8+t^9+t^10+t^11)

   /(-1+t)/(-1+t^5)/(-1+t^7)/(-1+t^11).

CROSSREFS

For the growth series for the finite group see A162496.

Sequence in context: A109678 A000330 A266783 * A211804 A283591 A238604

Adjacent sequences:  A266781 A266782 A266783 * A266785 A266786 A266787

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 11 2016

STATUS

approved

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Last modified May 30 03:33 EDT 2017. Contains 287305 sequences.