Binary Numbers Arranged

[Leroy Quet]

Max wrote
>Max wrote:
>> 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.)
>
>...
>
>> 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
>
>And 2 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 0 16
>
>Max


Hmmm.. I wonder if there are any more 2's in the sequence. (2 being the 
lowest possible positive value for the terms of the sequence past the 
first.)
It might make a fun puzzle to arrange (1 through n) so that no binary 
one's are next to each other, for some n where a(n) is low and positive.

thanks,
Leroy Quet