Question

Need help solving a recurrence definition in combinatorics:

Answer 1

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.

Answer 2

adding an x to a bad password would work, adding any other letter to a bad password would work

Answer 3

let a_n be the no of good pass words with n letters and b_n be the number of bad passwords with n letters.

a_n+b_n = (26)^n

a_(n+1) = 25*a_n + b_n
b_(n+1)= a_n +25 b_n ?

Answer 4

is it legal to define this way, or are we only allowed one variable

Answer 5

you can always eliminate b_n using the first equation

Answer 6

how would that look if you did it eliminating b_n