

A161699


Number of reduced words of length n in the Weyl group B_6.


22



1, 6, 20, 50, 104, 190, 315, 484, 699, 958, 1255, 1580, 1919, 2254, 2565, 2832, 3037, 3166, 3210, 3166, 3037, 2832, 2565, 2254, 1919, 1580, 1255, 958, 699, 484, 315, 190, 104, 50, 20, 6, 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
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OFFSET

0,2


COMMENTS

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


REFERENCES

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under PoincarĂ© polynomial.
N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)


LINKS

Table of n, a(n) for n=0..64.


FORMULA

G.f. for B_m is the polynomial Product_{k=1..m}(1x^(2k))/(1x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.


MATHEMATICA

CoefficientList[Series[(1  x^2) (1  x^4) (1  x^6) (1  x^8) (1  x^10) (1  x^12) / (1  x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 22 2016 *)


CROSSREFS

The growth series for the finite Coxeter (or Weyl) groups B_2 through B_12 are A161696A161699, A161716, A161717, A161733, A161755, A161776, A161858. These are all rows of A128084. The growth series for the affine Coxeter (or Weyl) groups B_2 through B_12 are A008576, A008137, A267167A267175.
Sequence in context: A063488 A299292 A162209 * A216175 A161409 A002415
Adjacent sequences: A161696 A161697 A161698 * A161700 A161701 A161702


KEYWORD

nonn


AUTHOR

John Cannon and N. J. A. Sloane, Nov 30 2009


STATUS

approved



