A135512 Number A(Bn,K) of all D-invariant ideals of the algebra NBn(K) of classical type over a field K if 2K=0.

2, 10, 41, 166, 670, 2700, 10869, 43718, 175730, 705988, 2835002, 11380060, 45666236, 183199832, 734768013, 2946348102, 11812385898, 47350033812, 189775422798, 760507313652, 3047308092708, 12209106348072, 48911419819458

Offset

1,1

Comments

The number A(Bn,K) of ideals of the maximal nilpotent subalgebra NBn(K) of the Chevalley algebra of the type Bn over an arbitrary field K of an order greater than 2 that are invariant under the subgroups D of all diagonal automorphisms is equal to C(2n,n) at 2K=K, n>1. If 2K=0: A(Bn,K)=a(n), n>=1.

References

G. P. Egorychev and V. M. Levchuk, Enumeration in the Chevalley algebras, ACM SIGSAM BulIetin, Vo135, No. 2, June 2001.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

G. P. Egorychev and V. M. Levchuk, Enumeration in the Chevalley algebras, ACM SIGSAM BulIetin, Vo135, No. 2, June 2001.

Formula

a(n) = 3*4^(n-1) - 2*binomial(2*(n-1),n-1)*(n*(n-1)+1)/(n*(n+1)).

Maple

seq(3*4^(n-1)-2*binomial(2*(n-1), n-1)*(n*(n-1)+1)/(n*(n+1)), n=1..30);

Mathematica

Table[3*4^(n - 1) - 2*Binomial[2*(n - 1), n - 1]*(n*(n - 1) + 1)/(n*(n + 1)), {n, 1, 25}] (* G. C. Greubel, Oct 17 2016 *)

Prog

(PARI) a(n)=3*4^(n-1) - 2*binomial(2*n-2, n-1)*(n^2-n+1)/(n^2+n) \\ Charles R Greathouse IV, Oct 17 2016

Crossrefs

Sequence in context: A197175 A297047 A037561 * A317328 A368678 A083937

Adjacent sequences: A135509 A135510 A135511 * A135513 A135514 A135515

Keyword

nonn

Author

Ehab Elbalawi (elb_ehab(AT)yahoo.com), Feb 09 2008

Status

approved