Passwords for a certain computer system are strings of uppercase letters. A valid password must contain an even number of X’s. Determine a recurrence relation for the number of valid passwords of length n.

Question

anonymous · Answer

I think we can find a formula by adding any non-X to the end of a good password of length n−1. That way the odd numbered passcodes have potential for two X's side by side...

anonymous · Answer

Does this look like a right start: 
Password with one slot = 25 
Password with two slots = 26 * 25 
Password with three slots = 26 * 26 * 25 
Password with four slots = 26 * 26 * 26