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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
1, 4, 14, 48, 167, 593, 2144, 7864, 29171, 109173, 411501, 1560089, 5943199, 22732739, 87253604, 335897864, 1296447899, 5015206349, 19439895089, 75487384829, 293595204239, 1143532045499, 4459774977449, 17413705988873 (list; graph; refs; listen; history; text; internal format)
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 * A014325 A047028 A220819

Adjacent sequences:  A007848 A007849 A007850 * A007852 A007853 A007854

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified October 28 17:19 EDT 2021. Contains 348329 sequences. (Running on oeis4.)