A161456 Number of reduced words of length n in the Weyl group A_8.

1, 8, 35, 111, 285, 628, 1230, 2191, 3606, 5545, 8031, 11021, 14395, 17957, 21450, 24584, 27073, 28675, 29228, 28675, 27073, 24584, 21450, 17957, 14395, 11021, 8031, 5545, 3606, 2191, 1230, 628, 285, 111, 35, 8, 1

Offset: 0

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Keywords

• nonn
• fini
• full

Comments

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

References

• J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
• N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche I.)

Crossrefs

Row n=9 of A008302.

Formula

G.f. for A_m is the polynomial Prod_{k=1..m}(1-x^(k+1))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A008302.