%I #14 Feb 18 2024 12:44:59

%S 1,12,77,353,1298,4070,11298,28468,66275,144430,297585,584255,1099879,

%T 1995478,3503742,5974816,9924564,16098676,25556652,39780455,60813480,

%U 91436445,135387879,197638068,284726628,405175311,569989222,793261337,1092897070,1491477647,2017283215,2705498950,3599629936,4753153273,6231438741,8113972406

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

%D 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).

%D J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.

%H Ray Chandler, <a href="/A266766/b266766.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_69">Index entries for linear recurrences with constant coefficients</a>, 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).

%F 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].

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

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jan 10 2016