

A161436


Number of reduced words of length n in the Weyl group A_4.


1



1, 4, 9, 15, 20, 22, 20, 15, 9, 4, 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
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OFFSET

0,2


COMMENTS

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..102.


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^5) / (1  x)^4, {x, 0, 20}], x] (* Vincenzo Librandi, Aug 23 2016 *)


CROSSREFS

Cf. A008302, A161409.
Sequence in context: A189388 A184916 A184931 * A274088 A189459 A301680
Adjacent sequences: A161433 A161434 A161435 * A161437 A161438 A161439


KEYWORD

nonn


AUTHOR

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


STATUS

approved



