A161776 Number of reduced words of length n in the Weyl group B_11.

1, 11, 65, 275, 934, 2706, 6941, 16159, 34749, 69927, 132991, 240901, 418198, 699258, 1130856, 1774992, 2711907, 4043193, 5894878, 8420346, 11802934, 16258034, 22034519, 29415309, 38716897, 50287667, 64504857, 81770051

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

G. C. Greubel, Table of n, a(n) for n = 0..121

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..11), x, 122), x, n), n = 0 .. 121); # Muniru A Asiru, Oct 25 2018

Mathematica

CoefficientList[Series[((1 - x^2) (1 - x^4) (1 - x^6) (1 - x^8) (1 - x^10) (1 - x^12) (1 - x^14) (1 - x^16) (1 - x^18) (1 - x^20) (1 - x^22)) / (1 - x)^11, {x, 0, 121}], x] (* Vincenzo Librandi, Aug 22 2016 *)

Prog

(PARI) t='t+O('t^40); Vec(prod(k=1, 11, 1-t^(2*k))/(1-t)^11) \\ G. C. Greubel, Oct 24 2018
(Magma) m:=40; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..11]])/(1-t)^11)); // G. C. Greubel, Oct 24 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: A332750 A161459 A162288 * A054333 A267173 A266765

Adjacent sequences: A161773 A161774 A161775 * A161777 A161778 A161779

Keyword

nonn,easy,fini,full

Author

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

Status

approved