A266767 Growth series for affine Coxeter group (or affine Weyl group) D_12.

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

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 (9, -36, 82, -108, 53, 90, -225, 217, -27, -217, 307, -153, -97, 179, 9, -270, 289, 28, -405, 431, 10, -558, 685, -218, -451, 702, -278, -433, 746, -363, -304, 538, -53, -687, 900, -270, -684, 1062, -459, -604, 1154, -703, -276, 818, -421, -468, 920, -468, -421, 818, -276, -703, 1154, -604, -459, 1062, -684, -270, 900, -687, -53, 538, -304, -363, 746, -433, -278, 702, -451, -218, 685, -558, 10, 431, -405, 28, 289, -270, 9, 179, -97, -153, 307, -217, -27, 217, -225, 90, 53, -108, 82, -36, 9, -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].