NL-NWO 2021 Problem 3

A frog jumps around on the grid points in the plane, from one grid point to another. The frog starts at the point $(0, 0)$ . Then it makes, successively, a jump of one step horizontally, a jump of $2$ steps vertically, a jump of $3$ steps horizontally, a jump of $4$ steps vertically, et cetera. Determine all $n > 0$ such that the frog can be back in $(0, 0)$ after $n$ jumps.