Associative magic square

An associative magic square is a magic square for which every pair of numbers symmetrically opposite to the center sum up to the same value.

3 × 3

The Lo Shu Square, the unique 3 × 3 normal magic square, is associative, and as such is the only 3 × 3 associative magic square. The square is shown below in Frénicle standard form. All rows, columns and diagonals sum to 15 and all pairs symmetrically opposite the center sum to 10.

276
951
438

4 × 4


There are 48 order four associative magic squares. [1] Dürer's associative magic square is shown below.[2]

gollark: I mostly use it for mildly patternmatchy ones, so it is irritating there.
gollark: But this niceness is reduced by all the `break`s.
gollark: I like `switch`es because they're nicer than just having a lot of `if` statements.
gollark: It is not strictly *necessary*, but nice to have, especially with Options and such (you've seen that in Rust right?).
gollark: No, I mean you could match on their contents.
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