Determine how many $100$-positive integer sequences satisfy the two conditions following: - At least one term of the sequence is equal to $4$ or $5$. - Any two adjacent terms differ as a maximum in $2$.
Source: Peru IMO TST 2016 p2
Tags: Integer sequence, Sequence, combinatorics
Determine how many $100$-positive integer sequences satisfy the two conditions following: - At least one term of the sequence is equal to $4$ or $5$. - Any two adjacent terms differ as a maximum in $2$.