Question 32
Let a natural number $n$ be given. Define $f(0, j)=f(i, 0)=0$, $f(1,1)=n$ and
$$
f(i, j)=\left\lfloor\frac{f(i-1, j)}{2}\right\rfloor+\left\lfloor\frac{f(i, j-1)}{2}\right\rfloor
$$
for all natural numbers $i$ and $j$, $(i, j) \neq (1,1)$. How many ordered pairs of natural numbers $(i, j)$ are there for which $f(i, j)$ is an odd number? (Dusan Djukic)
$$
f(i, j)=\left\lfloor\frac{f(i-1, j)}{2}\right\rfloor+\left\lfloor\frac{f(i, j-1)}{2}\right\rfloor
$$
for all natural numbers $i$ and $j$, $(i, j) \neq (1,1)$. How many ordered pairs of natural numbers $(i, j)$ are there for which $f(i, j)$ is an odd number? (Dusan Djukic)