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 A162367 Number of reduced words of length n in the Weyl group D_25. 31
 1, 25, 324, 2900, 20149, 115805, 572975, 2507895, 9904050, 35818770, 120016066, 376029250, 1110031585, 3106677225, 8286768736, 21161266240, 51931463950, 122883804990, 281186004075, 623785796595, 1344621849285, 2822018693325 (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..21. Index entries for growth series for groups FORMULA The growth series for D_k is the polynomial f(k)*Product_{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 f[m_] := (1-x^m)/(1-x); With[{k = 25}, CoefficientList[f[k]*Product[f[2i], {i, 1, k-1}] + O[x]^(k-3), x]] (* Jean-François Alcover, Feb 15 2023, after Maple code *) 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: A246625 A161525 A161932 * A263404 A077503 A262054 Adjacent sequences: A162364 A162365 A162366 * A162368 A162369 A162370 KEYWORD nonn AUTHOR John Cannon and N. J. A. Sloane, Dec 01 2009 STATUS approved

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Last modified December 6 17:01 EST 2023. Contains 367612 sequences. (Running on oeis4.)