A162399 Number of reduced words of length n in the Weyl group D_39.

1, 39, 779, 10621, 111149, 951899, 6946342, 44406362, 253761833, 1316306927, 6272724030, 27727887538, 114598003169, 445761614951, 1641026089535, 5744952627593, 19204564723487, 61521719896985, 189464360814690

Offset

0,2

Comments

Computed with MAGMA using commands similar to those used to compute A161409.

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..18.

Index entries for growth series for groups

Formula

G.f. for D_m is the polynomial f(n) * Product( f(2i), i=1..n-1 )/ f(1)^n, where f(k) = 1-x^k. Only finitely many terms are nonzero. This is a row of the triangle in 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: A010955 A161652 A162168 * A126927 A010991 A221358

Adjacent sequences: A162396 A162397 A162398 * A162400 A162401 A162402

Keyword

nonn

Author

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

Status

approved