A161698 Number of reduced words of length n in the Weyl group B_5.

1, 5, 14, 30, 54, 86, 125, 169, 215, 259, 297, 325, 340, 340, 325, 297, 259, 215, 169, 125, 86, 54, 30, 14, 5, 1

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 Poincaré polynomial.

N. Bourbaki, Groupes et algèbres. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

Links

Table of n, a(n) for n=0..25.

Formula

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

Maple

seq(coeff(series(mul((1-x^(2*k))/(1-x), k=1..5), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 25 2018

Mathematica

CoefficientList[Series[Product[(1-x^(2*k)), {k, 1, 5}] /(1-x)^5, {x, 0, 25}], x] (* G. C. Greubel, Oct 25 2018 *)

Prog

(PARI) t='t+O('t^26); Vec(prod(k=1, 5, 1-t^(2*k))/(1-t)^5) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=26; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..5]])/(1-t)^5)); // G. C. Greubel, Oct 25 2018

Crossrefs

The growth series for the finite Coxeter (or Weyl) groups B_2 through B_12 are A161696-A161699, 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, A267167-A267175.

Sequence in context: A231669 A256986 A162208 * A049791 A053461 A136135

Adjacent sequences: A161695 A161696 A161697 * A161699 A161700 A161701

Keyword

nonn,fini,full

Author

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

Status

approved