A267170 Growth series for affine Coxeter group B_7.

1, 8, 35, 113, 301, 700, 1471, 2857, 5209, 9016, 14940, 23856, 36897, 55504, 81481, 117055, 164941, 228412, 311373, 418440, 555023, 727414, 942880, 1209761, 1537573, 1937115, 2420581, 3001676, 3695738, 4519865, 5493047, 6636302, 7972817, 9528094, 11330100, 13409422, 15799426, 18536422, 21659833, 25212370, 29240211, 33793185, 38924961

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 (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).

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].