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A267175 Growth series for affine Coxeter group B_12.

%I A267175 #15 Feb 13 2024 14:50:09
%S A267175 1,13,90,443,1741,5811,17109,45577,111852,256282,553866,1138110,
%T A267175 2237924,4233126,7735923,13707967,23625303,39706809,65225654,
%U A267175 104927954,165588279,256738054,391610309,588352779,871571154,1274275456,1840315206,2627403376,3710845242,5188106314,7184373674,9859287465,13415044111,18106100284,24250736849
%N A267175 Growth series for affine Coxeter group B_12.
%D A267175 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 A267175 Ray Chandler, <a href="/A267175/b267175.txt">Table of n, a(n) for n = 0..1000</a>
%H A267175 <a href="/index/Rec#order_106">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 82, -108, 53, 90, -225, 217, -27, -217, 306, -144, -133, 261, -99, -217, 379, -197, -188, 404, -207, -252, 542, -360, -154, 521, -387, -107, 459, -326, -117, 358, -88, -452, 693, -327, -342, 666, -296, -434, 800, -415, -349, 720, -315, -460, 811, -359, -457, 800, -277, -649, 1102, -649, -277, 800, -457, -359, 811, -460, -315, 720, -349, -415, 800, -434, -296, 666, -342, -327, 693, -452, -88, 358, -117, -326, 459, -107, -387, 521, -154, -360, 542, -252, -207, 404, -188, -197, 379, -217, -99, 261, -133, -144, 306, -217, -27, 217, -225, 90, 53, -108, 82, -36, 9, -1).
%F A267175 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 A267175 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 A267175 nonn
%O A267175 0,2
%A A267175 _N. J. A. Sloane_, Jan 11 2016