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A162379 Number of reduced words of length n in the Weyl group D_32. 31
1, 32, 527, 5952, 51831, 370976, 2271896, 12237280, 59146604, 260441632, 1057250877, 3994502272, 14156055636, 47361532160, 150411609649, 455543049760, 1321024921186, 3680779823776, 9884216117666, 25650056954016 (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..19.

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: A084486 A161640 A161987 * A162739 A010984 A022596

Adjacent sequences:  A162376 A162377 A162378 * A162380 A162381 A162382

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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