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, 19348999600, 29245158395, 43578960064

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

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

Crossrefs

Row n=16 of A128084.

Programs

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

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.