A161987 Number of reduced words of length n in the Weyl group B_32.

1, 32, 527, 5952, 51831, 370976, 2271896, 12237280, 59146604, 260441632, 1057250877, 3994502272, 14156055636, 47361532160, 150411609649, 455543049760, 1321024921186, 3680779823776, 9884216117666, 25650056954016

Offset: 0

Author

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

Keywords

• nonn

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 II.)

Formula

G.f. for B_m is the polynomial Prod_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.