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 A162365 Number of reduced words of length n in the Weyl group D_23. 31
 1, 23, 275, 2277, 14673, 78407, 361514, 1477750, 5461235, 18518565, 58282576, 171815888, 477989151, 1262643305, 3183445871, 7694405993, 17895700206, 40182143330, 87349858045, 184297593435, 378236260170, 756560791350 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Differs from A161930 first at index n=23. - R. J. Mathar, Jul 12 2010 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..21. 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 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 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: A142027 A161523 A161930 * A162680 A010975 A022588 Adjacent sequences: A162362 A162363 A162364 * A162366 A162367 A162368 KEYWORD nonn,changed AUTHOR John Cannon and N. J. A. Sloane, Dec 01 2009 STATUS approved

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Last modified February 26 13:58 EST 2024. Contains 370352 sequences. (Running on oeis4.)