Domino and Tromino - Walkthrough

Tile a $2 \times n$ grid with dominoes and L-shaped trominoes. More tile $types = more$ transitions. $Width = 2$, so only $4$ masks: $00$, $01$, $10$, $11$.

Each mask transitions to several possible next masks. Enumerate: from mask $00$ (both empty), can place: horizontal domino (→ $00$), vertical domino in col $0$ (→ $10$), L-tromino (→ $01$ or $10$). Simplify: with width $2$, find a linear recurrence. $f[n] = 2f[n-1] + f[n-3]$. Closed form via matrix exponentiation.