OFFSET
0,2
REFERENCES
N. Bourbaki, Groupes et Algèbres 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
M. F. Hasler, Table of n, a(n) for n = 0..499
Index entries for linear recurrences with constant coefficients, signature (2, -1, 1, -2, 2, -2, 1, -1, 2, -1).
FORMULA
The growth series for the affine Coxeter group of type D_k (k >= 3) has g.f. = Product_i (1-x^{m_i+1})/((1-x)*(1-x^{m_i})) where the m_i are [1,3,5,...,2k-3,k-1].
Here (k=4) the g.f. is (t^3+1)*(1+t)*(1+t+t^2+t^3)^2/(-1+t^5)/(-1+t)^2/(-1+t^3).
PROG
(PARI) A266759_vec(N=100)=Vec((1+t='t)*(1+t^3+O(t^N))*(1+t+t^2+t^3)^2/(1-t)^2/(1-t^3)/(1-t^5)) \\ M. F. Hasler, Jul 12 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 10 2016
STATUS
approved