A182186 Number b(n) of basic ideals in the Borel subalgebra of the untwisted affine Lie algebra of type B.

24, 128, 648, 3160, 14984, 69536, 317264, 1427912, 6355080, 28021504, 122586224, 532681648, 2301267408, 9891512000, 42327269792, 180410129576, 766250022536, 3244192404032, 13696322822960, 57673821115088, 242287778611184, 1015664308220864, 4249246138360928

Offset

2,1

Comments

The corresponding sequence for the usual type B Lie algebra is given by the central binomial coefficients A000984.

Links

Table of n, a(n) for n=2..24.

J. Nilsson, Enumeration of basic ideals in type B

J. Nilsson, Enumeration of Basic Ideals in Type B Lie Algebras, J. Int. Seq. 15 (2012) #12.9.5

Formula

a(n) = (3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1).

a(n) - 8*a(n-1) + 16*a(n-2) = (24/(n-1))*binomial(2*n-6,n-2) for n>3.

-(n-1)*(9*n^2-51*n+76)*a(n) +2*(36*n^3-231*n^2+478*n-295)*a(n-1) -8*(2*n-5)*(9*n^2-33*n+34)*a(n-2)=0. - R. J. Mathar, Oct 27 2017

Maple

B:=n->(3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1): seq(B(n), n=2..30);

Prog

(PARI) a(n) = (3*n+5)*2^(2*n-2)-(2*(3*n-1))*binomial(2*n-2, n-1); \\ Michel Marcus, Aug 18 2013

Crossrefs

Cf. A000984, A194460.

Sequence in context: A044737 A305159 A326367 * A188304 A167981 A185490

Adjacent sequences: A182183 A182184 A182185 * A182187 A182188 A182189

Keyword

nonn,easy

Author

Jonathan Nilsson, Apr 16 2012

Status

approved