  To count the number of maximum independent arrangements of $n^2$ kings on a
$2n\times 2n$ chessboard, we build a $2^n \times (n+1)$ matrix whose entries
are independent arrangements of $n$ kings on $2\times 2n$ rectangles. Utilizing
upper and lower bound functions dependent of the entries of the matrix, we
recursively construct independent solutions, and provide a straight-forward
formula and algorithm.
