Leetcode 1411. Number of Ways to Paint N × 3 Grid

Count the number of ways to color an n×3 grid with 3 colors so that no two adjacent cells (horizontally or vertically) share a color, returning the result modulo 10^9+7. This is solved by dynamic programming over rows: there are 12 valid color patterns per row and you count transitions between patterns that avoid column-wise color matches.