An n×n magic square for which every pair of numbers symmetrically opposite the center sum to n^2 + 1. The Lo Shu is associative but not panmagic. The numbers of associative magic squares of order 1, 2, ... are 1, 0, 1, 48, ... (OEIS A081262). Order four squares can be panmagic or associative, but not both. Order five squares are the smallest which can be both associative and panmagic, and 16 distinct associative panmagic squares exist, one of which is illustrated above. The numbers of associative panmagic squares of order 1, 2, ... are therefore 1, 0, 0, 0, 16, ... (OEIS A081263).

magic square | panmagic square