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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

%I

%S 1,4,14,48,167,593,2144,7864,29171,109173,411501,1560089,5943199,

%T 22732739,87253604,335897864,1296447899,5015206349,19439895089,

%U 75487384829,293595204239,1143532045499,4459774977449,17413705988873

%N 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.

%H C. K. Fan, <a href="http://dx.doi.org/10.1023/A:1022443327568">A Hecke algebra quotient and some combinatorial applications</a>, J. Algebraic Combin. 5 (1996), no. 3, 175-189.

%H C. K. Fan, <a href="http://dx.doi.org/10.1090/S0894-0347-97-00222-1">Structure of a Hecke algebra quotient</a>, J. Amer. Math. Soc. 10 (1997), no. 1, 139-167.

%H J. R. Stembridge, <a href="http://dx.doi.org/10.1090/S0002-9947-97-01805-9">Some combinatorial aspects of reduced words in finite Coxeter groups</a>, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.

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

%t Table[(n+3) CatalanNumber[n]/2-1,{n,30}] (* _Harvey P. Dale_, Oct 06 2017 *)

%K nonn,easy

%O 1,2

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

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Last modified February 21 01:15 EST 2019. Contains 320364 sequences. (Running on oeis4.)