A267175 Growth series for affine Coxeter group B_12.

1, 13, 90, 443, 1741, 5811, 17109, 45577, 111852, 256282, 553866, 1138110, 2237924, 4233126, 7735923, 13707967, 23625303, 39706809, 65225654, 104927954, 165588279, 256738054, 391610309, 588352779, 871571154, 1274275456, 1840315206, 2627403376, 3710845242, 5188106314, 7184373674, 9859287465, 13415044111, 18106100284, 24250736849

Offset: 0

Author

N. J. A. Sloane, Jan 11 2016

Keywords

• nonn

References

• 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).

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, 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).

Crossrefs

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.

Formula

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].