%I #14 Feb 18 2024 12:40:53
%S 1,10,54,211,669,1827,4456,9942,20638,40357,75043,133663,229368,
%T 380976,614836,967138,1486741,2238597,3307855,4804735,6870266,9682988,
%U 13466724,18499534,25123969,33758748,44911987,59196114,77344609,100230715,128888272,164534832,208597219,262739703,328894963,409298018,506523312,623525146,763681655
%N Growth series for affine Coxeter group (or affine Weyl group) D_9.
%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="/A266764/b266764.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_43">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 34, -28, 0, 27, -27, 0, 27, -27, 1, 20, -5, -41, 77, -68, 22, 20, -26, 0, 27, -27, 0, 26, -20, -22, 68, -77, 41, 5, -20, -1, 27, -27, 0, 27, -27, 0, 28, -34, 21, -7, 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