A266765 Growth series for affine Coxeter group (or affine Weyl group) D_10.

1, 11, 65, 276, 945, 2772, 7228, 17170, 37807, 78156, 153164, 286714, 515781, 896057, 1509422, 2473703, 3955234, 6184807, 9477688, 14258463, 21091575, 30718516, 44102746, 62483525, 87439965, 120966735, 165562983, 224336176, 301122703, 400627235, 528582993, 691935236, 899050449, 1159953885, 1486598294, 1893166856, 2396413526, 3016044198

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 (7, -21, 34, -28, -1, 34, -48, 34, 0, -35, 56, -62, 57, -41, 15, 15, -39, 43, -19, -20, 50, -61, 57, -43, 28, -22, 21, -16, 12, -17, 26, -30, 26, -17, 12, -16, 21, -22, 28, -43, 57, -61, 50, -20, -19, 43, -39, 15, 15, -41, 57, -62, 56, -35, 0, 34, -48, 34, -1, -28, 34, -21, 7, -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: A161776 A054333 A267173 * A036601 A125321 A054490

Adjacent sequences: A266762 A266763 A266764 * A266766 A266767 A266768

Keyword

nonn

Author

N. J. A. Sloane, Jan 10 2016

Status

approved