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A162209 Number of reduced words of length n in the Weyl group D_6. 0
1, 6, 20, 50, 104, 190, 314, 478, 679, 908, 1151, 1390, 1605, 1776, 1886, 1924, 1886, 1776, 1605, 1390, 1151, 908, 679, 478, 314, 190, 104, 50, 20, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
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..73.

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

The growth series for D_k, k >= 5, are A162208-A162212, A162248, A162288, A162297.

The growth series for D_k, k >= 3, are also the rows of the triangle A162206.

Sequence in context: A161438 A063488 A299292 * A161699 A216175 A161409

Adjacent sequences:  A162206 A162207 A162208 * A162210 A162211 A162212

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 19 22:00 EDT 2018. Contains 316378 sequences. (Running on oeis4.)