A 'bitstring' is a string consisting of 0s and 1s. However, you're only looking for bitstrings with the following properties:
- There are no two consecutive 1's in the bitstring.
- Every run of 0's is of even length (i.e. every block of 0's has an even number of 0's in it).
1001 is an example of such a bitstring, but 10001 is not. Luckily, your computer science (or combinatorics) teacher shares a formula for figuring out how many such bitstrings exist for any given length N:
- s(0) = 1, s(1) = 1, s(2) = 1.
- s(n) = s(n-2) + s(n-3) for all n > 2.
That is, there is only 1 string of size 0 (empty string matches both rules), only 1 string of size 1 ("1"), and only 1 string of size 2 ("00"). For size 3, you'd need to calculate the sum of s(3-2) and s(3-3), which are known from the results above.
The input file DATA3.txt will contain 5 test cases, each being a line with a single integer 1 <= N <= 75, the length of the bitstring.
The output file OUT3.txt will contain 5 lines of output, each being the number of different bitstrings of the corresponding length N with the described properties.