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%I #15 Feb 13 2024 14:36:12
%S 1,6,20,51,110,211,372,615,966,1455,2117,2991,4120,5551,7334,9524,
%T 12180,15365,19146,23594,28784,34795,41711,49619,58611,68783,80234,
%U 93067,107389,123312,140952,160430,181870,205400,231152,259261,289867,323114,359151,398131,440211,485551,534315,586672,642794,702858,767045,835540,908532,986214
%N Growth series for affine Coxeter group B_5.
%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="/A267168/b267168.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1, 0, 0, 0, 1, -3, 4, -4, 3, -1, 0, 0, 0, -1, 3, -3, 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].
%F Here (k=5) the G.f. is -(1+t)*(1+t+t^2+t^3)*(t^3+1)*(1+t+t^2+t^3+t^4+t^5+t^6+t^7)*(t^5+1)/(-1+t^9)/(-1+t^7)/(-1+t)^3.
%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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