A161900 Number of reduced words of length n in the Weyl group B_22.

1, 22, 252, 2002, 12396, 63734, 283107, 1116236, 3983485, 13057330, 39764011, 113533312, 306173263, 784654154, 1920802566, 4510960122, 10201294213, 22286443124, 47167714715, 96947735390, 193938666735, 378324531180, 720920510115, 1344018408150, 2454841642634

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 II.)

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..484

Crossrefs

Row n=22 of A128084.

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.