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A161699
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Number of reduced words of length n in the Weyl group B_6.
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22
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1, 6, 20, 50, 104, 190, 315, 484, 699, 958, 1255, 1580, 1919, 2254, 2565, 2832, 3037, 3166, 3210, 3166, 3037, 2832, 2565, 2254, 1919, 1580, 1255, 958, 699, 484, 315, 190, 104, 50, 20, 6, 1
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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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J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
N. Bourbaki, Groupes et algèbres de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)
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LINKS
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FORMULA
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G.f. for B_m is the polynomial Product_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.
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MAPLE
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seq(coeff(series(mul((1-x^(2*k))/(1-x), k=1..6), x, n+1), x, n), n = 0 .. 36); # Muniru A Asiru, Oct 25 2018
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MATHEMATICA
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CoefficientList[Series[(1 - x^2) (1 - x^4) (1 - x^6) (1 - x^8) (1 - x^10) (1 - x^12) / (1 - x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 22 2016 *)
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PROG
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(PARI) t='t+O('t^40); Vec(prod(k=1, 6, 1-t^(2*k))/(1-t)^6) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=40; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..6]])/(1-t)^6)); // G. C. Greubel, Oct 25 2018
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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