A161876 Number of reduced words of length n in the Weyl group B_16.

1, 16, 135, 800, 3739, 14672, 50252, 154224, 432174, 1121456, 2724183, 6248128, 13624922, 28409312, 56910017, 109964720, 205651975, 373334400, 659553555, 1136450288, 1913567669, 3154109024, 5096972454, 8086166144, 12609525259

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 II.)

Links

Robert Israel, Table of n, a(n) for n = 0..256 (complete sequence)

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.

Maple

G:= normal(mul((1-x^(2*k))/(1-x), k=1..16)):
seq(coeff(G, x, j), j=0..256); # Robert Israel, Mar 31 2017

Crossrefs

Sequence in context: A284338 A161477 A162327 * A110274 A067814 A219904

Adjacent sequences: A161873 A161874 A161875 * A161877 A161878 A161879

Keyword

nonn,fini,full

Author

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

Status

approved