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 A162297 Number of reduced words of length n in the Weyl group D_12. 32
 1, 12, 77, 352, 1286, 3992, 10933, 27092, 61841, 131768, 264759, 505660, 923857, 1623104, 2753895, 4528612, 7239585, 11280072, 17168009, 25572196, 37340381, 53528488, 75430016, 104604424, 142903123, 192491532, 255865533, 335860592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. Bourbaki, Groupes et Algèbres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10a, page 231, W(t). J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial. LINKS Table of n, a(n) for n=0..27. 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; MATHEMATICA n = 12; x = y + y O[y]^(n^2); (1-x^n) Product[1-x^(2k), {k, 1, n-1}]/(1-x)^n // CoefficientList[#, y]& (* Jean-François Alcover, Mar 25 2020, from A162206 *) CROSSREFS The growth series for D_k, k >= 3, are also the rows of the triangle A162206. Growth series for groups D_n, n = 3,...,50: 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, A162380, A162381, A162384, A162388, A162389, A162392, A162399, A162402, A162403, A162411, A162412, A162413, A162418, A162452, A162456, A162461, A162469, A162492; also A162206. Sequence in context: A335253 A071767 A161461 * A161858 A054334 A267174 Adjacent sequences: A162294 A162295 A162296 * A162298 A162299 A162300 KEYWORD nonn,changed AUTHOR John Cannon and N. J. A. Sloane, Dec 01 2009 EXTENSIONS Entry revised by N. J. A. Sloane, Jan 17 2016 STATUS approved

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Last modified February 28 03:01 EST 2024. Contains 370379 sequences. (Running on oeis4.)