login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182186 Number b(n) of basic ideals in the Borel subalgebra of the untwisted affine Lie algebra of type B. 0
24, 128, 648, 3160, 14984, 69536, 317264, 1427912, 6355080, 28021504, 122586224, 532681648, 2301267408, 9891512000, 42327269792, 180410129576, 766250022536, 3244192404032, 13696322822960, 57673821115088, 242287778611184, 1015664308220864, 4249246138360928 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 15:16 EDT 2020. Contains 333107 sequences. (Running on oeis4.)