Binary Numbers Arranged

[Max]

Max wrote:
> Leroy Quet wrote:
>> 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?
> 
> I've got
> 1 2 0 4 2 0 0 0 8 32 0 8 0 0 0 0 0 64 0 1968

With 3 more terms:
1 2 0 4 2 0 0 0 8 32 0 8 0 0 0 0 0 64 0 1968 508 0 0

Max