A162469 Number of reduced words of length n in the Weyl group D_49.

1, 49, 1224, 20776, 269499, 2848811, 25555215, 200037215, 1394396185, 8790665065, 50733161116, 270672378844, 1345758869770, 6277354061930, 27627446293371, 115285643098059, 458048619713020, 1739199358769180

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..17.

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: A163005 A161694 A162204 * A011001 A269418 A115999

Adjacent sequences: A162466 A162467 A162468 * A162470 A162471 A162472

Keyword

nonn

Author

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

Status

approved