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A266767 Growth series for affine Coxeter group (or affine Weyl group) D_12. 10
1, 13, 90, 443, 1741, 5811, 17109, 45577, 111852, 256282, 553866, 1138111, 2237936, 4233203, 7736276, 13709265, 23629373, 39718107, 65254122, 104994229, 165732709, 257035638, 392194554, 589452604, 873566421, 1277778529, 1846288195, 2637323484, 3726933976, 5213642329, 7224113781, 9920025945, 13506347040, 18241259200, 24447994900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.

LINKS

Table of n, a(n) for n=0..34.

FORMULA

The growth series for the affine Coxeter group of type D_k (k >= 3) has G.f. = (1-x^{m_k})/((1-x)*Prod_i (1-x^{m_i})) where the m_i are [1,3,5,...,2k-3,k-1].

CROSSREFS

The growth series for the affine Coxeter groups D_3 through D_12 are A005893 and A266759-A266767.

Sequence in context: A161859 A057788 A267175 * A166215 A296574 A131700

Adjacent sequences:  A266764 A266765 A266766 * A266768 A266769 A266770

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 10 2016

STATUS

approved

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Last modified September 18 20:18 EDT 2019. Contains 327181 sequences. (Running on oeis4.)