

A161435


Number of reduced words of length n in the Weyl group A_3.


0



1, 3, 5, 6, 5, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET

0,2


COMMENTS

a(n) is also the number of vertices of a truncated octahedron (the Voronoi cell for the lattice A_3*) at edge distance n from a given vertex. See also row 4 of the triangle in A008302.  N. J. A. Sloane, Oct 12 2015, corrected Aug 26 2016.
If the zeros are omitted, this is the coordination sequence for the truncated octahedron (see Karzes link).  N. J. A. Sloane, Jan 08 2020
Computed with MAGMA using commands similar to those used to compute A161409.


REFERENCES

N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche I.)
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under PoincarĂ© polynomial.


LINKS

Table of n, a(n) for n=0..104.
Tom Karzes, Polyhedron Coordination Sequences


FORMULA

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


MATHEMATICA

CoefficientList[Series[(1  x^2) (1  x^3) (1  x^4) / (1  x)^3, {x, 0, 20}], x] (* Vincenzo Librandi, Aug 23 2016 *)


CROSSREFS

Cf. A008302, A161409.
Sequence in context: A106117 A081498 A110279 * A224831 A281591 A267884
Adjacent sequences: A161432 A161433 A161434 * A161436 A161437 A161438


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



