LeetCode 790 Domino and Tromino Tiling - Problem Statement

Tile a $2 \times n$ board with two tile types: $1 \times 2$ dominoes (horizontal or vertical) and L-shaped trominoes (each covering $3$ cells). Count the number of tilings modulo $10^9 + 7$, where $n$ can be up to $1000$. Trominoes add new profile states: you can have one row sticking out one cell further than the other.

This creates profiles you didn't see with dominoes alone. With $n$ up to $1000$, you need an $O(n)$ time, $O(1)$ space solution. Broken profile DP with $2$ rows gives you states and formulas that lead to a recurrence.