There are 5 zeroes and 5 ones in this sequence.

The longest string of ones is 4.

The longest string of zeroes is 2.

The difference in string lengths is 2.

Create a sequence consisting of 100 zeroes and 100 ones which maximizes the difference in lengths between the longest string of 1's and the longest string of 0's.

Find a formula for the maximum difference in string lengths with n zeroes and n ones.