AMC 12 2022a Problem 5

The taxicab distance between points $(x_1, y_1)$ and $(x_2, y_2)$ in the coordinate plane is given by $$|x_1 - x_2| + |y_1 - y_2|.$$ For how many points $P$ with integer coordinates is the taxicab distance between $P$ and the origin less than or equal to $20$?

\textbf{(A)} 441 \textbf{(B)} 761 \textbf{(C)} 841 \textbf{(D)} 921 \textbf{(E)} 924