Figures $0$, $1$, $2$, and $3$ consist of $1$, $5$, $13$, and $25$ nonoverlapping unit squares, respectively. If the pattern were continued, how many nonoverlapping unit squares would there be in figure 100?


$\textbf{(A)}\ 10401 \qquad\textbf{(B)}\ 19801 \qquad\textbf{(C)}\ 20201 \qquad\textbf{(D)}\ 39801 \qquad\textbf{(E)}\ 40801$
We can attempt $0^2+1^2=1$ and $1^2+2^2=5$, so the pattern here looks like the number of squares in the $n$-th figure is $n^2+(n+1)^2$*. When we plug in 100 for $n$, we get $100^2+101^2=10000+10201=20201$, or option $\textbf{(C)}$.