# DWITE Online Computer Programming Contest

## Bitstrings

November 2012
Problem 3

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 1s in the bitstring.
• Every run of 0s is of even length (i.e. every block of 0s has an even number of 0s 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.

Sample Input (first 2 shown):
```1
20```
Sample Output (first 2 shown):
```1
200```