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A161696
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Number of reduced words of length n in the Weyl group B_3.
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22
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1, 3, 5, 7, 8, 8, 7, 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
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OFFSET
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0,2
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COMMENTS
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If the zeros are ignored, this is the coordination sequence for the truncated cuboctahedron (see the Karzes link). - N. J. A. Sloane, Jan 08 2020
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 Prod_{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^(2k))/(1-x), k=1..3), x, n+1), x, n), n = 0 .. 120); # Muniru A Asiru, Oct 25 2018
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MATHEMATICA
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CoefficientList[Series[Product[(1-x^(2*k)), {k, 1, 3}] /(1-x)^3, {x, 0, 9}], x] (* G. C. Greubel, Oct 25 2018 *)
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PROG
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(PARI) t='t+O('t^10); Vec(prod(k=1, 3, 1-t^(2*k))/(1-t)^3) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=10; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..3]])/(1-t)^3)); // G. C. Greubel, Oct 25 2018
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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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