A267169 Growth series for affine Coxeter group B_6.

1, 7, 27, 78, 188, 399, 771, 1386, 2352, 3807, 5924, 8916, 13041, 18606, 25971, 35554, 47835, 63361, 82750, 106695, 135968, 171425, 214011, 264764, 324820, 395417, 477900, 573724, 684459, 811795, 957546, 1123655, 1312198, 1525389, 1765583, 2035281, 2337134, 2673948, 3048689, 3464488, 3924646, 4432636, 4992108, 5606893, 6281008, 7018660

Offset

0,2

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 (4, -6, 3, 3, -6, 3, 4, -10, 10, -4, -2, 2, 3, -6, 3, 2, -2, -4, 10, -10, 4, 3, -6, 3, 3, -6, 4, -1).

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].

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.

Sequence in context: A162493 A005585 A161410 * A266761 A027180 A036597

Adjacent sequences: A267166 A267167 A267168 * A267170 A267171 A267172

Keyword

nonn

Author

N. J. A. Sloane, Jan 11 2016

Status

approved