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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
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 Poincaré polynomial.
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.
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
Sequence in context: A313221 A313222 A313223 * A274088 A313224 A313225
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Nov 30 2009
STATUS
approved