Siamese method
Put number 1 in the middle of the top row. Put the numbers 2 up to n (= length of the square) each time one cell diagonal up and to the right. Put number n+1 below number n. Put the numbers n+2 up to 2n each time one cell diagonal up and to the right. Put number 2n+1 below number 2n. Etcetera ...
9x9 symmetric magic square
| 47 | 58 | 69 | 80 | 1 | 12 | 23 | 34 | 45 |
| 57 | 68 | 79 | 9 | 11 | 22 | 33 | 44 | 46 |
| 67 | 78 | 8 | 10 | 21 | 32 | 43 | 54 | 56 |
| 77 | 7 | 18 | 20 | 31 | 42 | 53 | 55 | 66 |
| 6 | 17 | 19 | 30 | 41 | 52 | 63 | 65 | 76 |
| 16 | 27 | 29 | 40 | 51 | 62 | 64 | 75 | 5 |
| 26 | 28 | 39 | 50 | 61 | 72 | 74 | 4 | 15 |
| 36 | 38 | 49 | 60 | 71 | 73 | 3 | 14 | 25 |
| 37 | 48 | 59 | 70 | 81 | 2 | 13 | 24 | 35 |
You can use this method to construct magic squares of odd order from 3x3 to infinite and you get a symmetric (but not pan)magic square.
See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29 and 31x31
