A161636 Number of reduced words of length n in the Weyl group A_31.

1, 31, 495, 5424, 45848, 318649, 1895464, 9919009, 46584724, 199347764, 786519756, 2888400232, 9950014727, 32360135292, 99903188872, 294134516323, 829176461458, 2245909515022, 5862798149046, 14789460753680, 36138546144580

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..20.

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: A022626 A042866 A110824 * A161977 A162378 A162737

Adjacent sequences: A161633 A161634 A161635 * A161637 A161638 A161639

Keyword

nonn

Author

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

Status

approved