A266762 Growth series for affine Coxeter group (or affine Weyl group) D_7.

1, 8, 35, 113, 301, 700, 1472, 2864, 5236, 9094, 15128, 24255, 37669, 56896, 83853, 120913, 170975, 237539, 324787, 437668, 581987, 764501, 993020, 1276513, 1625220, 2050768, 2566292, 3186562, 3928115, 4809392, 5850881, 7075264, 8507569, 10175328, 12108740, 14340839, 16907667, 19848452, 23205791, 27025840, 31358509, 36257661

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

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

Sequence in context: A040977 A266785 A267170 * A220889 A285240 A036598

Adjacent sequences: A266759 A266760 A266761 * A266763 A266764 A266765

Keyword

nonn

Author

N. J. A. Sloane, Jan 10 2016

Status

approved