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 A162328 Number of reduced words of length n in the Weyl group D_17. 32
 1, 17, 152, 952, 4691, 19363, 69615, 223839, 656013, 1777469, 4501652, 10749780, 24374702, 52784014, 109694031, 219658751, 425310726, 798645125, 1458198664, 2594648817, 4508215686, 7662320971, 12759278753, 20845394645, 33454765680 (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 Poincaré polynomial. LINKS Table of n, a(n) for n=0..24. Index entries for growth series for groups 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: A244852 A064102 A161497 * A161877 A221737 A139617 Adjacent sequences: A162325 A162326 A162327 * A162329 A162330 A162331 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 01 2009 STATUS approved

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Last modified February 21 04:08 EST 2024. Contains 370219 sequences. (Running on oeis4.)