A palindrome is a string whose reversal is identical to the string. How many bit string of length n are palindromes?

A string of length n can be either even or odd. The definition of the palindrome forces the first half of the string to equal the second half with the special of case of the odd numbered palindrome to have a central number that isn't equvalent to anything.

Thus the number of even palindromes are 2^n/2

and the number of odd palindromes are 2