TxO Math Bowl 2024 - Individuals A - Problem 14

Let N be the number of strings of length 7 such that each character is in the set \{A, B, C, D\}, and that given any four consecutive characters from the string, they are not all distinct. Find the remainder when N is divided by 100.

(For example, ABCBBDA is valid, as out of ABCB, BCBB, CBBD, and BBDA, each of them contain at least one duplicate letter, but ABCDABB is invalid, because the letters in BCDA are all distinct.)