2-dimensional version of Fibonacci numbers

[Edwin Clark]

On Sat, 15 Nov 2003, Yuval Dekel wrote:

> Let a(m,n) = number of mXn (0,1) matrices that have no consecutive
> horizontal or vertical  0's.
> 
> So a(1,n)=a(n,1) are the Fibonacci numbers - A000045 .
> 
> Is there a formula for a(n,n) ?
> 

See 

http://www.research.att.com/projects/OEIS?Anum=A006506

I agree with the first 4 terms there: 1,7,63,1234. I don't know about the
rest, but there is something wrong with the Maple program given there. It
doesn't produce the sequence. And the sequence it does produce apparently
is not in the EIS.

--Edwin