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A162211 Number of reduced words of length n in the Weyl group D_8. 0
1, 8, 35, 112, 293, 664, 1350, 2520, 4388, 7208, 11263, 16848, 24248, 33712, 45425, 59480, 75853, 94384, 114766, 136544, 159125, 181800, 203777, 224224, 242318, 257296, 268504, 275440, 277788, 275440, 268504, 257296, 242318, 224224, 203777 (list; graph; refs; listen; history; text; internal format)
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..34.

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

The growth series for D_k, k >= 5, are A162208-A162212, A162248, A162288, A162297.

The growth series for D_k, k >= 3, are also the rows of the triangle A162206.

Sequence in context: A006600 A161456 A005732 * A161717 A162494 A040977

Adjacent sequences:  A162208 A162209 A162210 * A162212 A162213 A162214

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)