A162380 Number of reduced words of length n in the Weyl group D_33.

1, 33, 560, 6512, 58343, 429319, 2701215, 14938495, 74085099, 334526731, 1391777608, 5386279880, 19542335516, 66903867676, 217315477325, 672858527085, 1993883448271, 5674663272047, 15558879389713, 41208936343729

Offset

0,2

Comments

Computed with MAGMA using commands similar to those used to compute A161409.

References

N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.)

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.

Links

Table of n, a(n) for n=0..19.

Index entries for growth series for groups

Formula

G.f. for D_m is the polynomial f(n) * Product( f(2i), i=1..n-1 )/ f(1)^n, where f(k) = 1-x^k. Only finitely many terms are nonzero. This is a row of the triangle in A162206.

Crossrefs

Growth series for groups D_n, n = 3,...,50: A161435, A162207, A162208, A162209, A162210, A162211, A162212, A162248, A162288, A162297, A162300, A162301, A162321, A162327, A162328, A162346, A162347, A162359, A162360, A162364, A162365, A162366, A162367, A162368, A162369, A162370, A162376, A162377, A162378, A162379, A162380, A162381, A162384, A162388, A162389, A162392, A162399, A162402, A162403, A162411, A162412, A162413, A162418, A162452, A162456, A162461, A162469, A162492; also A162206.

Sequence in context: A010949 A161646 A161988 * A188357 A126923 A010985

Adjacent sequences: A162377 A162378 A162379 * A162381 A162382 A162383

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 01 2009

Status

approved