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A162212 Number of reduced words of length n in the Weyl group D_9. 10
1, 9, 44, 156, 449, 1113, 2463, 4983, 9372, 16587, 27877, 44802, 69231, 103314, 149425, 210075, 287796, 384999, 503812, 645906, 812319, 1003290, 1218116, 1455045, 1711216, 1982655, 2264333, 2550288, 2833809, 3107676, 3364445 (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..30.

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

A162212g := proc(m::integer)

    (1-x^m)/(1-x) ;

end proc:

A162212 := proc(n, k)

    g := A162212g(k);

    for m from 2 to 2*k-2 by 2 do

        g := g*A162212g(m) ;

    end do:

    g := expand(g) ;

    coeftayl(g, x=0, n) ;

end proc:

seq( A162212(n, 9), n=0..30) ; # R. J. Mathar, Jan 19 2016

MATHEMATICA

n = 9;

x = y + y O[y]^(n^2);

(1-x^n) Product[1-x^(2k), {k, 1, n-1}]/(1-x)^n // CoefficientList[#, y]& (* Jean-François Alcover, Mar 25 2020, from 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: A034194 A075206 A161457 * A161733 A050486 A267176

Adjacent sequences:  A162209 A162210 A162211 * A162213 A162214 A162215

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified June 4 04:39 EDT 2020. Contains 334815 sequences. (Running on oeis4.)