2022 AMC 12A 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 \qquad\textbf{(B)} \, 761 \qquad\textbf{(C)} \, 841 \qquad\textbf{(D)} \, 921 \qquad\textbf{(E)} \, 924

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.