HMMT November 2021 U30

The function $f: \mathbb{Z}^{2} \rightarrow \mathbb{Z}$ satisfies

• $f(x, 0)=f(0, y)=0$, and
• $f(x, y)=f(x-1, y)+f(x, y-1)+x+y$ for all nonnegative integers $x$ and $y$. Find $f(6,12)$.