Combinations: String possibilities

This is somewhat more related to mathematics but since it is a problem as well, choosing to ask the question.
A binary string is a string containing only two characters, 0s and 1s.

Input: n.

We want to find out all possible combinations of 0s and 1s in a string of length ‘n’ where 0s have to be adjacent in multiples of 2. Whereas 1s can be adjacent in multiples of 1.
e.g. 111001(n=6) & 10000(n=5) fits in the required criteria but 110100(n=6) does not because at position 3, there is only 1 zero and adjacence is 1 which is not a multiple of 2.

Output: number of possible combinations.

I can not figure out how to solve this problem. Please give me some hint or starting point so I can work on it.