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Growth series for affine Coxeter group B_7.
1

%I #16 Feb 13 2024 14:40:27

%S 1,8,35,113,301,700,1471,2857,5209,9016,14940,23856,36897,55504,81481,

%T 117055,164941,228412,311373,418440,555023,727414,942880,1209761,

%U 1537573,1937115,2420581,3001676,3695738,4519865,5493047,6636302,7972817,9528094,11330100,13409422,15799426,18536422,21659833,25212370,29240211,33793185,38924961

%N Growth series for affine Coxeter group B_7.

%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="/A267170/b267170.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 9, 0, -9, 9, 0, -9, 10, -5, 2, -5, 11, -14, 10, 0, -9, 9, 0, -10, 14, -11, 5, -2, 5, -10, 9, 0, -9, 9, 0, -9, 10, -5, 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