Put digit 1 in the middle of the top row. Put the digits 2 up to n (= length of the square) each time one cell diagonal up and to the right. Put digit n+1 below digit n. Put the digits n+2 up to 2n each time one cell diagonal up and to the right. Put digit 2n+1 below digit 2n. Etcetera ...
5x5 symmetric magic square
17 | 24 | 1 | 8 | 15 |
23 | 5 | 7 | 14 | 16 |
4 | 6 | 13 | 20 | 22 |
10 | 12 | 19 | 21 | 3 |
11 | 18 | 25 | 2 | 9 |
You can use this method to construct magic squares of odd order from 3x3 to infinite and you get symmetric (but not pan)magic squares.