A266764 Growth series for affine Coxeter group (or affine Weyl group) D_9.

1, 10, 54, 211, 669, 1827, 4456, 9942, 20638, 40357, 75043, 133663, 229368, 380976, 614836, 967138, 1486741, 2238597, 3307855, 4804735, 6870266, 9682988, 13466724, 18499534, 25123969, 33758748, 44911987, 59196114, 77344609, 100230715, 128888272, 164534832, 208597219, 262739703, 328894963, 409298018, 506523312, 623525146, 763681655

Offset: 0

Author

N. J. A. Sloane, Jan 10 2016

Keywords

• nonn

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 (7, -21, 34, -28, 0, 27, -27, 0, 27, -27, 1, 20, -5, -41, 77, -68, 22, 20, -26, 0, 27, -27, 0, 26, -20, -22, 68, -77, 41, 5, -20, -1, 27, -27, 0, 27, -27, 0, 28, -34, 21, -7, 1).

Crossrefs

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

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].