A267173 Growth series for affine Coxeter group B_10.

1, 11, 65, 276, 945, 2772, 7228, 17170, 37807, 78155, 153154, 286660, 515570, 895388, 1507595, 2469247, 3945292, 6164170, 9437339, 14183455, 20958025, 30489449, 43722470, 61870160, 86475684, 119485204, 163333410, 221043295, 296341927, 393794113, 518955998, 678550795, 880669001, 1134995618, 1453067068, 1848560666, 2337619696, 2939217322

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 (7, -21, 34, -28, -1, 34, -48, 34, -1, -28, 35, -28, 29, -42, 49, -33, -5, 42, -46, 8, 43, -66, 43, 7, -39, 21, 29, -62, 55, -30, 22, -44, 74, -71, 18, 52, -84, 52, 18, -71, 74, -44, 22, -30, 55, -62, 29, 21, -39, 7, 43, -66, 43, 8, -46, 42, -5, -33, 49, -42, 29, -28, 35, -28, -1, 34, -48, 34, -1, -28, 34, -21, 7, -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].