A007851 Number of elements w of the Weyl group D(n) such that the roots sent negative by w span an Abelian subalgebra of the Lie algebra.

1, 4, 14, 48, 167, 593, 2144, 7864, 29171, 109173, 411501, 1560089, 5943199, 22732739, 87253604, 335897864, 1296447899, 5015206349, 19439895089, 75487384829, 293595204239, 1143532045499, 4459774977449, 17413705988873

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Boothby, T.; Burkert, J.; Eichwald, M.; Ernst, D. C.; Green, R. M.; Macauley, M.  On the cyclically fully commutative elements of Coxeter groups, J. Algebr. Comb. 36, No. 1, 123-148 (2012), Table 1 FC Type D.

C. K. Fan, A Hecke algebra quotient and some combinatorial applications, J. Algebraic Combin. 5 (1996), no. 3, 175-189.

C. K. Fan, Structure of a Hecke algebra quotient, J. Amer. Math. Soc. 10 (1997), no. 1, 139-167.

J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.

Formula

a(n) = (n+3)*C(n)/2 - 1, where C(n) is a Catalan number (see A000108).

D-finite with recurrence: -(n+1)*(3*n^2+n-12)*a(n) +(15*n^3+14*n^2-85*n+36)*a(n-1) -2*(2*n-3)*(3*n^2+7*n-8)*a(n-2)=0. - R. J. Mathar, Jun 11 2019

Mathematica

Table[(n+3) CatalanNumber[n]/2-1, {n, 30}] (* Harvey P. Dale, Oct 06 2017 *)

Crossrefs

Sequence in context: A071757 A082590 A085280 * A368555 A014325 A047028

Adjacent sequences: A007848 A007849 A007850 * A007852 A007853 A007854

Keyword

nonn,easy

Author

C. Kenneth Fan [ ckfan(AT)MIT.EDU ]

Status

approved