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 A161697 Number of reduced words of length n in the Weyl group B_4. 0
 1, 4, 9, 16, 24, 32, 39, 44, 46, 44, 39, 32, 24, 16, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Computed with MAGMA using commands similar to those used to compute A161409. REFERENCES 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.) LINKS Table of n, a(n) for n=0..99. FORMULA 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. MAPLE seq(coeff(series(mul((1-x^(2k))/(1-x), k=1..4), x, n+1), x, n), n = 0 .. 100); # Muniru A Asiru, Oct 25 2018 MATHEMATICA CoefficientList[Series[Product[(1-x^(2*k)), {k, 1, 4}] /(1-x)^4, {x, 0, 16}], x] (* G. C. Greubel, Oct 25 2018 *) PROG (PARI) t='t+O('t^17); Vec(prod(k=1, 4, 1-t^(2*k))/(1-t)^4) \\ G. C. Greubel, Oct 25 2018 (Magma) m:=17; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..4]])/(1-t)^4)); // G. C. Greubel, Oct 25 2018 CROSSREFS The growth series for the finite Coxeter (or Weyl) groups B_2 through B_12 are A161696-A161699, A161716, A161717, A161733, A161755, A161776, A161858. These are all rows of A128084. The growth series for the affine Coxeter (or Weyl) groups B_2 through B_12 are A008576, A008137, A267167-A267175. Sequence in context: A122986 A066427 A320891 * A078593 A168350 A281151 Adjacent sequences: A161694 A161695 A161696 * A161698 A161699 A161700 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Nov 30 2009 STATUS approved

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Last modified May 23 14:23 EDT 2024. Contains 372763 sequences. (Running on oeis4.)