A267171 Growth series for affine Coxeter group B_8.

1, 9, 44, 157, 458, 1158, 2629, 5486, 10695, 19711, 34651, 58507, 95404, 150908, 232389, 349445, 514393, 742832, 1054283, 1472911, 2028333, 2756518, 3700784, 4912897, 6454277, 8397316, 10826813, 13841530, 17555875, 22101717, 27630339, 34314534, 42350849, 51961982, 63399337, 76945741, 92918329, 111671603, 133600669, 159144658, 188790335

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 (5, -10, 9, 0, -9, 9, 0, -9, 10, -5, 2, -5, 11, -14, 11, -5, 1, 0, 0, -1, 5, -11, 14, -12, 10, -12, 14, -11, 5, -1, 0, 0, 1, -5, 11, -14, 11, -5, 2, -5, 10, -9, 0, 9, -9, 0, 9, -10, 5, -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: A161733 A050486 A267176 * A266763 A213755 A036599

Adjacent sequences: A267168 A267169 A267170 * A267172 A267173 A267174

Keyword

nonn

Author

N. J. A. Sloane, Jan 11 2016

Status

approved