A161475 Number of reduced words of length n in the Weyl group A_14.

1, 14, 104, 545, 2260, 7889, 24087, 66013, 165425, 384320, 836604, 1720774, 3366951, 6301715, 11333950, 19664205, 33018831, 53808313, 85306779, 131846699, 199019426, 293868698, 425060810, 603012233, 839953393, 1149906518, 1548556267, 2052994543, 2681325612

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

Andrew Howroyd, Table of n, a(n) for n = 0..105

Formula

G.f. for A_m is the polynomial Product_{k=1..m} (1-x^(k+1))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A008302.

Maple

b:= proc(u, o) option remember; expand(`if`(u+o=0, 1,
       add(b(u+j-1, o-j)*x^(u+j-1), j=1..o)+
       add(b(u-j, o+j-1)*x^(u-j), j=1..u)))
    end:
coeffs(b(15, 0));  # Alois P. Heinz, Mar 21 2025

Mathematica

b[u_, o_] := b[u, o] = Expand[If[u+o == 0, 1, Sum[b[u+j-1, o-j]*x^(u+j-1), {j, 1, o}] + Sum[b[u-j, o+j-1]*x^(u-j), {j, 1, u}]]];
CoefficientList[b[15, 0], x] (* Jean-François Alcover, May 16 2025, after Alois P. Heinz *)

Crossrefs

Row n=15 of A008302.

Sequence in context: A295210 A255721 A089508 * A162301 A161862 A266561

Adjacent sequences: A161472 A161473 A161474 * A161476 A161477 A161478

Keyword

nonn,fini,full

Author

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

Status

approved