Binary Numbers Arranged

[Leroy Quet]

What is the sequence where the nth term, a(n), is the number of 
permutations of (1,2,3,...,n) written in binary so that no adjacent 
elements share a common 1-bit?

In other words, if b(m) and b(m+1) are adjacent elements written in 
binary,
then (b(m) AND b(m+1)) = 0 for 1 <= m <= n-1.
(If a logical AND is applied to each pair of adjacent terms, the result 
is zero.)

I get, as done by hand, the sequence:
1,2,0,4,2,0,0,0,0,20,...

If I did not make a mistake, and I very well could have, this sequence is 
not yet in the EIS.

Could someone please calculate/submit the sequence if it is not yet in 
the EIS?

Additional sequences, which may or may not already be in the EIS:
The first and last terms of the permutations must AND to zero as well.
The permutations counted are of (0,1,2,...n), starting at 0 instead of at 
1.

By the way, figuring out by hand that the 10th term is 20 (if it really 
is) was a fun and not too difficult challenge, using reasoning similar to 
that used to solve an easy sudoku puzzle.

Thanks,
Leroy Quet