A200613 Number of quasi-abelian ideals in the affine Lie algebra sl_n^{hat}.

1, 3, 11, 44, 183, 774, 3294, 14034, 59711, 253430, 1072506, 4525168, 19036726, 79861404, 334155036, 1394789214, 5808981711, 24143440374, 100156051746, 414762312504, 1714844273586, 7079573497524, 29187378344676, 120180109515204, 494264431607718, 2030539136846844

Offset: 1

Author

N. J. A. Sloane, Nov 19 2011

Keywords

• nonn

Comments

Christian Krattenthaler has shown that a(n)=((n+4)/4)*binomial(2*n,n)-3*2^(2*n-3). This implies that a(n)=A194460(n) - A000531(n-1). The latter fact was first empirically observed by D. S. McNeil. [Volodymyr Mazorchuk, Sep 14 2012]

Links

• Karin Baur and Volodymyr Mazorchuk, Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras, arXiv:1108.3659 [math.RA]

Programs

PARI

a(n) = ((n+4)/4)*binomial(2*n,n)-3*2^(2*n-3);

Formula

a(n) = ((n+4)/4)*binomial(2*n,n)-3*2^(2*n-3). [Volodymyr Mazorchuk, Sep 14 2012]