Let a_{n} denote the number of ternary strings of length n so that there does not exist a k<n such that the first k digits of the string equals the last k digits. What is the largest integer m such that 3^{m} \mid a_{2023}?
Let a_{n} denote the number of ternary strings of length n so that there does not exist a k<n such that the first k digits of the string equals the last k digits. What is the largest integer m such that 3^{m} \mid a_{2023}?