With the Lozenge method of John Horton Conway you get a magic square of odd order and you find all odd numbers in the (white) 'diamond' and all even numbers outside the diamond (in the dark area). See for detailed explanation: Lozenge 5x5 magic square.

Take 1x number from row grid +1

+ 17x number from column grid

= 17x17 Lozenge magic square

Use this method to construct magic squares of odd order (= 3x3, 5x5, 7x7, ... magic square).

See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27,   29x29 and 31x31