A267172 Growth series for affine Coxeter group B_9.

1, 10, 54, 211, 669, 1827, 4456, 9942, 20637, 40348, 74999, 133506, 228910, 379818, 612207, 961652, 1476045, 2218878, 3273169, 4746115, 6774561, 9531380, 13232864, 18147232, 24604366, 33006891, 43842720, 57699190, 75278921, 97417535, 125103378, 159499393, 201967298, 254094228, 317722005, 394979205, 488316197, 600543335, 734872490

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 (6, -15, 19, -9, -9, 18, -9, -9, 18, -9, -8, 12, 7, -34, 43, -25, -2, 11, 6, -28, 27, 0, -27, 26, 6, -43, 52, -26, -5, 5, 26, -52, 43, -6, -26, 27, 0, -27, 28, -6, -11, 2, 25, -43, 34, -7, -12, 8, 9, -18, 9, 9, -18, 9, 9, -19, 15, -6, 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: A162248 A161755 A053347 * A266764 A036600 A058645

Adjacent sequences: A267169 A267170 A267171 * A267173 A267174 A267175

Keyword

nonn

Author

N. J. A. Sloane, Jan 11 2016

Status

approved