How to generate a list of palindromes with only 'x','y' and a given length n in Python?

Question

is there any patterns i can use to sort out how to create a string that is palindrome which made up with 'X' 'Y'

Answer 1

Let's assume n is even. Generate every string of length n/2 that consists of x and y, and append its mirror image to get a palindrome.

Exercise 1: prove that this generates all palindromes of length n.

Exercise 2: figure out what to do when n is odd.