A161858 Number of reduced words of length n in the Weyl group B_12.

1, 12, 77, 352, 1286, 3992, 10933, 27092, 61841, 131768, 264759, 505660, 923858, 1623116, 2753972, 4528964, 7240871, 11284064, 17178942, 25599288, 37402222, 53660256, 75694775, 105110084, 143826980, 194114636, 258619428, 340389204

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..144

Formula

G.f. for B_m is the polynomial Product_{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^(2k))/(1-x), k=1..12), x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 25 2018

Mathematica

CoefficientList[Series[Product[(1-x^(2*k)), {k, 1, 12}]/(1-x)^12, {x, 0, 50}], x] (* G. C. Greubel, Oct 25 2018 *)

Prog

(PARI) t='t+O('t^50); Vec(prod(k=1, 12, 1-t^(2*k))/(1-t)^12) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=50; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..12]])/(1-t)^12)); // 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: A071767 A161461 A162297 * A054334 A267174 A266766

Adjacent sequences: A161855 A161856 A161857 * A161859 A161860 A161861

Keyword

nonn

Author

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

Status

approved