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 ...
11x11 symmetric magic square
68 | 81 | 94 | 107 | 120 | 1 | 14 | 27 | 40 | 53 | 66 |
80 | 93 | 106 | 119 | 11 | 13 | 26 | 39 | 52 | 65 | 67 |
92 | 105 | 118 | 10 | 12 | 25 | 38 | 51 | 64 | 77 | 79 |
104 | 117 | 9 | 22 | 24 | 37 | 50 | 63 | 76 | 78 | 91 |
116 | 8 | 21 | 23 | 36 | 49 | 62 | 75 | 88 | 90 | 103 |
7 | 20 | 33 | 35 | 48 | 61 | 74 | 87 | 89 | 102 | 115 |
19 | 32 | 34 | 47 | 60 | 73 | 86 | 99 | 101 | 114 | 6 |
31 | 44 | 46 | 59 | 72 | 85 | 98 | 100 | 113 | 5 | 18 |
43 | 45 | 58 | 71 | 84 | 97 | 110 | 112 | 4 | 17 | 30 |
55 | 57 | 70 | 83 | 96 | 109 | 111 | 3 | 16 | 29 | 42 |
56 | 69 | 82 | 95 | 108 | 121 | 2 | 15 | 28 | 41 | 54 |
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