Count distinct palindromic subsequences

Given a string `s` consisting of lowercase English letters, compute how many **distinct palindromic subsequence strings** of lengths **2**, **3**, and **4** can be formed from `s`. A subsequence is formed by deleting zero or more characters without changing the relative order of the remaining characters. Count palindromes by their resulting string value, **not** by the number of index combinations. For example, if the same palindrome can be formed in multiple ways, it should be counted only once. Return three values: 1. the number of distinct palindromic subsequences of length 2, 2. the number of distinct palindromic subsequences of length 3, 3. the number of distinct palindromic subsequences of length 4. Examples of valid palindromes include `aa` for length 2, `aba` for length 3, and `abba` or `aaaa` for length 4.