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%I #16 Feb 13 2024 14:44:00
%S 1,10,54,211,669,1827,4456,9942,20637,40348,74999,133506,228910,
%T 379818,612207,961652,1476045,2218878,3273169,4746115,6774561,9531380,
%U 13232864,18147232,24604366,33006891,43842720,57699190,75278921,97417535,125103378,159499393,201967298,254094228,317722005,394979205,488316197,600543335,734872490
%N Growth series for affine Coxeter group B_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).
%H Ray Chandler, <a href="/A267172/b267172.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_59">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 19, -9, -9, 18, -9, -9, 18, -9, -8, 12, 7, -34, 43, -25, -2, 11, 6, -28, 27, 0, -27, 26, 6, -43, 52, -26, -5, 5, 26, -52, 43, -6, -26, 27, 0, -27, 28, -6, -11, 2, 25, -43, 34, -7, -12, 8, 9, -18, 9, 9, -18, 9, 9, -19, 15, -6, 1).
%F The growth series for the affine Coxeter group of type B_k (k >= 2) 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-1].
%Y The growth series for the finite Coxeter (or Weyl) groups B_2 through B_12 are A161696-A161699, A161716, A161717, A161733, A161755, A161776, A161858. These are all rows of A128084. The growth series for the affine Coxeter (or Weyl) groups B_2 through B_12 are A008576, A008137, A267167-A267175.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jan 11 2016
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