Codeforces 478D Red Green Towers - Base Cases

Before building any levels, you've used $0$ red blocks in exactly one way (by doing nothing). $dp[0][0] = 1$. For any $j > 0$: $dp[0][j] = 0$. You can't use red blocks without building any levels.

From here, iterate through levels $i = 1, 2, \dots, h$ and apply the transition. After processing all levels, sum $dp[h][j]$ for every valid $j$ to get the total number of ways to color the tower.