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A162208 Number of reduced words of length n in the Weyl group D_5. 9
1, 5, 14, 30, 54, 85, 120, 155, 185, 205, 212, 205, 185, 155, 120, 85, 54, 30, 14, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (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 algèbres 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..91.

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.

MAPLE

A162208g := proc(m::integer)

    (1-x^m)/(1-x) ;

end proc:

A162208 := proc(n, k)

    g := A162208g(k);

    for m from 2 to 2*k-2 by 2 do

        g := g*A162208g(m) ;

    end do:

    g := expand(g) ;

    coeftayl(g, x=0, n) ;

end proc:

seq( A162208(n, 5), n=0..60) ; # R. J. Mathar, Jan 19 2016

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: A076042 A231669 A256986 * A161698 A049791 A053461

Adjacent sequences:  A162205 A162206 A162207 * A162209 A162210 A162211

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified November 19 06:26 EST 2019. Contains 329310 sequences. (Running on oeis4.)