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A162378 Number of reduced words of length n in the Weyl group D_31. 31
1, 31, 495, 5425, 45879, 319145, 1900920, 9965384, 46909324, 201295028, 796809245, 2937251395, 10161553364, 33205476524, 103050077489, 305131440111, 865481871426, 2359754902590, 6203436293890, 15765840836350, 38828731002622 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..20.

Index entries for growth series for groups


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.


# 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;


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: A110824 A161636 A161977 * A162737 A010983 A022595

Adjacent sequences:  A162375 A162376 A162377 * A162379 A162380 A162381




John Cannon and N. J. A. Sloane, Dec 01 2009



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Last modified October 16 07:07 EDT 2021. Contains 348041 sequences. (Running on oeis4.)