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A266767 Growth series for affine Coxeter group (or affine Weyl group) D_12.

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%I A266767 #13 Feb 18 2024 12:47:06
%S A266767 1,13,90,443,1741,5811,17109,45577,111852,256282,553866,1138111,
%T A266767 2237936,4233203,7736276,13709265,23629373,39718107,65254122,
%U A266767 104994229,165732709,257035638,392194554,589452604,873566421,1277778529,1846288195,2637323484,3726933976,5213642329,7224113781,9920025945,13506347040,18241259200,24447994900
%N A266767 Growth series for affine Coxeter group (or affine Weyl group) D_12.
%D A266767 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 A266767 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.
%H A266767 Ray Chandler, <a href="/A266767/b266767.txt">Table of n, a(n) for n = 0..1000</a>
%H A266767 <a href="/index/Rec#order_94">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 82, -108, 53, 90, -225, 217, -27, -217, 307, -153, -97, 179, 9, -270, 289, 28, -405, 431, 10, -558, 685, -218, -451, 702, -278, -433, 746, -363, -304, 538, -53, -687, 900, -270, -684, 1062, -459, -604, 1154, -703, -276, 818, -421, -468, 920, -468, -421, 818, -276, -703, 1154, -604, -459, 1062, -684, -270, 900, -687, -53, 538, -304, -363, 746, -433, -278, 702, -451, -218, 685, -558, 10, 431, -405, 28, 289, -270, 9, 179, -97, -153, 307, -217, -27, 217, -225, 90, 53, -108, 82, -36, 9, -1).
%F A266767 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 A266767 The growth series for the affine Coxeter groups D_3 through D_12 are A005893 and A266759-A266767.
%K A266767 nonn
%O A266767 0,2
%A A266767 _N. J. A. Sloane_, Jan 10 2016