A266766 Growth series for affine Coxeter group (or affine Weyl group) D_11.

1, 12, 77, 353, 1298, 4070, 11298, 28468, 66275, 144430, 297585, 584255, 1099879, 1995478, 3503742, 5974816, 9924564, 16098676, 25556652, 39780455, 60813480, 91436445, 135387879, 197638068, 284726628, 405175311, 569989222, 793261337, 1092897070, 1491477647, 2017283215, 2705498950, 3599629936, 4753153273, 6231438741, 8113972406

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 (8, -28, 55, -62, 28, 27, -54, 27, 27, -54, 27, 27, -53, 19, 56, -117, 118, -64, 10, -10, 63, -110, 89, -1, -81, 81, 0, -82, 89, -29, -18, -11, 99, -173, 173, -99, 11, 18, 29, -89, 82, 0, -81, 81, 1, -89, 110, -63, 10, -10, 64, -118, 117, -56, -19, 53, -27, -27, 54, -27, -27, 54, -27, -28, 62, -55, 28, -8, 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].

Crossrefs

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

Sequence in context: A161858 A054334 A267174 * A026964 A026974 A210695

Adjacent sequences: A266763 A266764 A266765 * A266767 A266768 A266769

Keyword

nonn

Author

N. J. A. Sloane, Jan 10 2016

Status

approved