Question 42
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 $f(6,12)$.
- $f(x, 0) = f(0, y) = 0$, and
- $f(x, y) = f(x-1, y) + f(x, y-1) + x + y$
for all nonnegative integers $x$ and $y$. Find $f(6,12)$.