Maximum arrangements of nonattacking kings on the 2n × 2n chessboard

To count the number of maximum independent arrangements of n² kings on a 2n × 2n chessboard, we build a 2ⁿ × (n + 1) matrix whose entries are independent arrangements of n kings on 2 × 2n rectangles. Utilizing upper and lower bound functions dependent of the entries of the matrix, we recursively construct independent solutions, and provide an equation and algorithm.