Suppose our coordinate is (x, y). Every time we move, we increase x + y by 3.

Thus, we will make (x + y) / 3 moves in order to reach (x, y).

Every time we move 1 tile right and 1 tile down. We don't choose that. What we choose is if we move 1 extra tile right or 1 extra tile down.

Suppose (x + y) / 3 = k. Then we need to choose to move extra tile down x — k times and extra tile right the rest of the times (which is equal to y — k times).

Now we're just left to choose which exactly times we will choose to go down. We can choose any set of x — k turns of total k turns. So the answer is either 0 or C_k_(x-k).