all columns, rows, diagonals in a list...

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(defun all-magic-square-lines (n)
  (let ((alist (magic-square n)))
      (append alist
            (loop for x from 0 to (1- (length (car alist)))
                          collect (loop for i in alist
                                        collect (nth x i)))

            (list (loop for i in alist
                  with cnt = 0
                  collect (nth cnt i)
                  do (incf cnt)))
            
            
            (list (loop for i in alist
                  with cnt = (1- (length (car alist)))
                  collect (nth cnt i)
              do (decf cnt))))))
    
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(all-magic-square-lines 3)
=> ((8 1 6) (3 5 7) (4 9 2) (8 3 4) (1 5 9) (6 7 2) (8 5 2) (6 5 4))

(all-magic-square-lines 4)
=> ((16 5 9 4) (2 11 7 14) (3 10 6 15) (13 8 12 1) (16 2 3 13) (5 11 10 8) (9 7 6 12) (4 14 15 1) (16 11 6 1) (4 7 10 13)) 

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;; test
(loop for i in (all-magic-square-rows 7)
        collect (sum i))
=> (175 175 175 175 175 175 175 175 175)

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(all-magic-square-lines 3)

Cool !