I have N numbers in an array A. The numbers are either 0 or 1 and given that A[1]=0 as well as A[N]=0.
In every operation the array changes as follows:
- If a cell has two adjacent values that are both equal, then the value becomes 1.
- Otherwise it becomes 0.
- First and last cells always remain 0.
Example:
[0,0,1,0,1,0]
[0,0,1,1,1,0]
[0,0,0,1,0,0]
[0,1,0,1,0,0]
[0,1,1,1,0,0]
[0,0,1,0,0,0]
[0,0,1,0,1,0]
Is is possible to derive a general formula f(N) for the number of iteration after which the pattern will repeat itself.