A162369 Number of reduced words of length n in the Weyl group D_27.

1, 27, 377, 3627, 27026, 166230, 878409, 4098483, 17222607, 66165501, 235124461, 780112671, 2435132466, 7196829486, 20245295242, 54455027238, 140596223184, 349621224120, 839832229131, 1953829030737, 4412447681628, 9693085025844

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)*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,...,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: A257786 A161530 A161954 * A231858 A341564 A162726

Adjacent sequences: A162366 A162367 A162368 * A162370 A162371 A162372

Keyword

nonn

Author

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

Status

approved