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
Ray Chandler, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1, 0, 0, 0, 1, -5, 11, -15, 15, -11, 5, -1, 0, 0, 0, -1, 5, -10, 10, -5, 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=7) the G.f. is -(1+t+t^2+t^3)*(1+t)*(1+t+t^2+t^3+t^4+t^5+t^6+t^7)*(t^5+1)*(t^9+t^6+t^3+1)/(-1+t^11)/(-1+t^9)/(-1+t)^5.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 10 2016
STATUS
approved