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

1,2

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

Table of n, a(n) for n=1..26.

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

Formula

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

Prog

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

Crossrefs

Sequence in context: A239392 A122393 A012880 * A149073 A167011 A319322

Adjacent sequences: A200610 A200611 A200612 * A200614 A200615 A200616

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2011

Status

approved