A computer system considers a string, whose characters are taken from English lowercase alphabets from a to m (total 13 alphabets), a valid code if the alphabet 'a' occurs an even number of times in the string. For example, "jeildmaabi" is a valid code, whereas "jeildmacbi" is not a valid code. Let 'a' be the number of valid codes consisting of 'n' characters. Derive the recursive relation for 'a_n' for 'n' ≥ 2. Specify the value of 'a_1'. [4M]