A discrete uniform on $2n+1$ points: $Y=4$ means $X=\pm2$

Let X be a discrete r.v. with the following pmf: $P[X=x]=k$ for $x=0,\pm j$, $j=1,2,\dots,n$, and $0$ otherwise. Let $Y=X^2$, then $P[Y=4]$ is: