TITLE: Minimum number of moves to reach a cell in a chessboard by a knight
QUESTION [17 upvotes]: Given an infinite chessboard represented as a 2D Cartesian plane. A knight is placed at the origin. What is the minimum number of moves it needs to reach a cell $(m,n)$? (Without loss of generality, we might as well assume that $m$ and $n$ are nonnegative integers.)

REPLY [2 votes]: The answers are tabulated here at the Online Encyclopedia of Integer Sequences. A formula is also given there, but it has a recursive component: for $m$ and $n$ at least 2, it gives $$T(m,n)=1+\min(T(m-2,n-1),T(m-1,n-2))$$ You could work on turning that into a closed form.