For a nonnegative order, first enumerate every possible row and then every possible ordered selection of rows:
squares :: Int -> [[[Int]]]
squares n
  | n < 0     = error "negative order"
  | otherwise = cp (replicate n (cp (replicate n [1..n])))
Every one of the positions chooses one of symbols independently. Consequently the enumeration contains candidate squares for , each exactly once. The conventional order-zero extension produces one empty square. This is generation only; repeated symbols have not yet been rejected.

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