A266761 - OEIS

%I #14 Feb 18 2024 12:35:13

%S 1,7,27,78,188,400,777,1406,2403,3917,6136,9293,13670,19603,27485,

%T 37773,50993,67744,88703,114628,146366,184857,231139,286352,351742,

%U 428669,518610,623164,744055,883138,1042406,1223994,1430184,1663408,1926254,2221471,2551974,2920848,3331353,3786930,4291206,4847999,5461321,6135384,6874604

%N Growth series for affine Coxeter group (or affine Weyl group) D_6.

%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="/A266761/b266761.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 3, 3, -5, -1, 10, -13, 7, 2, -6, 2, 7, -13, 10, -1, -5, 3, 3, -6, 4, -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].

%F Here (k=6) the G.f. is (t^5+1)*(1+t+t^2+t^3+t^4+t^5+t^6+t^7)*(1+t+t^2+t^3)*(1+t)*(t^3+1)^2/(t^7-t^6+t^4-t^3+t-1)/(-1+t^7)/(-1+t)^3/(-1+t^5).

%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