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A161858
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Number of reduced words of length n in the Weyl group B_12.
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22
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1, 12, 77, 352, 1286, 3992, 10933, 27092, 61841, 131768, 264759, 505660, 923858, 1623116, 2753972, 4528964, 7240871, 11284064, 17178942, 25599288, 37402222, 53660256, 75694775, 105110084, 143826980, 194114636, 258619428, 340389204
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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^(2k))/(1-x), k=1..12), x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 25 2018
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MATHEMATICA
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CoefficientList[Series[Product[(1-x^(2*k)), {k, 1, 12}]/(1-x)^12, {x, 0, 50}], x] (* G. C. Greubel, Oct 25 2018 *)
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PROG
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(PARI) t='t+O('t^50); Vec(prod(k=1, 12, 1-t^(2*k))/(1-t)^12) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=50; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..12]])/(1-t)^12)); // 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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