A162411 Number of reduced words of length n in the Weyl group D_42.

1, 42, 902, 13202, 148091, 1357468, 10587675, 72245074, 440091498, 2430433874, 12315996232, 57824666110, 253554446677, 1045266952884, 4073988274266, 15084671038416, 53281879968821, 180187334962466, 585265396834041

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..18.

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: A296011 A161663 A162179 * A010994 A229564 A004422

Adjacent sequences: A162408 A162409 A162410 * A162412 A162413 A162414

Keyword

nonn

Author

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

Status

approved