Advent calendar 2025

Valid sequences of length \(n\) can be made by doing one of the following:

Therefore, the number of sequences of length \(n\) that end in B is equal to the total number of sequences of length \(n-1\); and the number of sequences of length \(n\) that end in A is equal to the number of sequences of length \(n-1\) that end in B plus the number of sequences of length \(n-2\) that end in A. Using this we see that:

The total number of valid sequences of length 11 is 638.