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 A162369 Number of reduced words of length n in the Weyl group D_27. 31
 1, 27, 377, 3627, 27026, 166230, 878409, 4098483, 17222607, 66165501, 235124461, 780112671, 2435132466, 7196829486, 20245295242, 54455027238, 140596223184, 349621224120, 839832229131, 1953829030737, 4412447681628, 9693085025844 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.) J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under PoincarĂ© polynomial. LINKS FORMULA The growth series for D_k is the polynomial f(k)*Prod_{i=1..k-1} f(2*i), where f(m) = (1-x^m)/(1-x) [Corrected by N. J. A. Sloane, Aug 07 2021]. This is a row of the triangle in A162206. MAPLE # Growth series for D_k, truncated to terms of order M. - N. J. A. Sloane, Aug 07 2021 f := proc(m::integer) (1-x^m)/(1-x) ; end proc: g := proc(k, M) local a, i; global f; a:=f(k)*mul(f(2*i), i=1..k-1); seriestolist(series(a, x, M+1)); end proc; CROSSREFS Growth series for groups D_n, n = 3,...,32: A161435, A162207, A162208, A162209, A162210, A162211, A162212, A162248, A162288, A162297, A162300, A162301, A162321, A162327, A162328, A162346, A162347, A162359, A162360, A162364, A162365, A162366, A162367, A162368, A162369, A162370, A162376, A162377, A162378, A162379; also A162206 Sequence in context: A257786 A161530 A161954 * A231858 A341564 A162726 Adjacent sequences:  A162366 A162367 A162368 * A162370 A162371 A162372 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 01 2009 STATUS approved

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Last modified July 4 23:17 EDT 2022. Contains 355086 sequences. (Running on oeis4.)