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 A161776 Number of reduced words of length n in the Weyl group B_11. 22
 1, 11, 65, 275, 934, 2706, 6941, 16159, 34749, 69927, 132991, 240901, 418198, 699258, 1130856, 1774992, 2711907, 4043193, 5894878, 8420346, 11802934, 16258034, 22034519, 29415309, 38716897, 50287667, 64504857, 81770051 (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 G. C. Greubel, Table of n, a(n) for n = 0..121 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^(2*k))/(1-x), k=1..11), x, 122), x, n), n = 0 .. 121); # Muniru A Asiru, Oct 25 2018 MATHEMATICA CoefficientList[Series[((1 - x^2) (1 - x^4) (1 - x^6) (1 - x^8) (1 - x^10) (1 - x^12) (1 - x^14) (1 - x^16) (1 - x^18) (1 - x^20) (1 - x^22)) / (1 - x)^11, {x, 0, 121}], x] (* Vincenzo Librandi, Aug 22 2016 *) PROG (PARI) t='t+O('t^40); Vec(prod(k=1, 11, 1-t^(2*k))/(1-t)^11) \\ G. C. Greubel, Oct 24 2018 (MAGMA) m:=40; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..11]])/(1-t)^11)); // G. C. Greubel, Oct 24 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: A332750 A161459 A162288 * A054333 A267173 A266765 Adjacent sequences:  A161773 A161774 A161775 * A161777 A161778 A161779 KEYWORD nonn,easy,fini,full AUTHOR John Cannon and N. J. A. Sloane, Nov 30 2009 STATUS approved

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Last modified July 14 05:39 EDT 2020. Contains 335716 sequences. (Running on oeis4.)