A161640 Number of reduced words of length n in the Weyl group A_32.

1, 32, 527, 5951, 51799, 370448, 2265912, 12184921, 58769645, 258117409, 1044637165, 3933037397, 13883052124, 46243187416, 146146376288, 440280892611, 1269457354069, 3515366869091, 9378165018137, 24167625771817

Offset

0,2

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.)

Links

Table of n, a(n) for n=0..19.

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.

Crossrefs

Sequence in context: A146124 A125489 A084486 * A161987 A162379 A162739

Adjacent sequences: A161637 A161638 A161639 * A161641 A161642 A161643

Keyword

nonn

Author

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

Status

approved