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
KEYWORD
nonn
AUTHOR
Ehab Elbalawi (elb_ehab(AT)yahoo.com), Feb 09 2008
STATUS
approved