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A161436
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Number of reduced words of length n in the Weyl group A_4.
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1
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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
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0,2
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COMMENTS
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Computed with MAGMA using commands similar to those used to compute A161409.
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REFERENCES
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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.
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LINKS
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FORMULA
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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