A266765 - OEIS

%I #15 Feb 18 2024 12:42:55

%S 1,11,65,276,945,2772,7228,17170,37807,78156,153164,286714,515781,

%T 896057,1509422,2473703,3955234,6184807,9477688,14258463,21091575,

%U 30718516,44102746,62483525,87439965,120966735,165562983,224336176,301122703,400627235,528582993,691935236,899050449,1159953885,1486598294,1893166856,2396413526,3016044198

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

%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="/A266765/b266765.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_64">Index entries for linear recurrences with constant coefficients</a>, 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).

%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