The 15x15 magic square is odd but also a multiple of 3. You can use the shift method to construct a 15x15 magic square but with boundary condition. Take as first row of the first and/or
second grid 0-1-2-3-4-5-6-7- 8-9-10-11-12-13-14, than you get only a semi-magic 15x15 square. Take as first row of the first and/or second
grid 0-2-1-3-4-5-8-7-6-11-10-9-13-12-14, and you get a panmagic 15x15 square.
The row 0-2-1-3-4-5-8-7-6-11-10-9-13-12-14 leads to a valid
15x15 panmagic square because 0+3+8+11+13 = 2+4+7+10+12 = 1+5+6+9+14 = 35, that is 1/3 of (0+1+2+3+4+5+6+7+8 +9+10+11+12+13+14=) 105.
Take 1x number from first grid (shift 2 to the left) +1
0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 |
1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 |
4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 |
8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 |
6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 |
10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 |
13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 |
14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 |
2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 |
3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 |
5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 |
7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 |
11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 |
9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 |
12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 |
+15x number from second grid (shift 2 to the right)
0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 |
12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 |
9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 |
11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 |
7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 |
5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 |
3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 |
2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 |
14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 |
13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 |
10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 |
6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 | 8 | 7 |
8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 | 4 | 5 |
4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 | 1 | 3 |
1 | 3 | 4 | 5 | 8 | 7 | 6 | 11 | 10 | 9 | 13 | 12 | 14 | 0 | 2 |
= panmagic 15x15 square
1 | 33 | 17 | 49 | 65 | 81 | 129 | 113 | 97 | 177 | 161 | 145 | 209 | 193 | 225 |
182 | 214 | 5 | 36 | 24 | 53 | 67 | 87 | 131 | 115 | 104 | 178 | 165 | 136 | 198 |
140 | 201 | 189 | 218 | 7 | 42 | 26 | 55 | 74 | 88 | 135 | 106 | 93 | 167 | 154 |
174 | 158 | 142 | 207 | 191 | 220 | 14 | 43 | 30 | 46 | 63 | 77 | 124 | 110 | 96 |
112 | 102 | 176 | 160 | 149 | 208 | 195 | 211 | 3 | 32 | 19 | 50 | 66 | 84 | 128 |
86 | 130 | 119 | 103 | 180 | 151 | 138 | 197 | 184 | 215 | 6 | 39 | 23 | 52 | 72 |
59 | 73 | 90 | 121 | 108 | 92 | 169 | 155 | 141 | 204 | 188 | 217 | 12 | 41 | 25 |
45 | 16 | 48 | 62 | 79 | 125 | 111 | 99 | 173 | 157 | 147 | 206 | 190 | 224 | 13 |
213 | 2 | 34 | 20 | 51 | 69 | 83 | 127 | 117 | 101 | 175 | 164 | 148 | 210 | 181 |
199 | 185 | 216 | 9 | 38 | 22 | 57 | 71 | 85 | 134 | 118 | 105 | 166 | 153 | 137 |
156 | 144 | 203 | 187 | 222 | 11 | 40 | 29 | 58 | 75 | 76 | 123 | 107 | 94 | 170 |
98 | 172 | 162 | 146 | 205 | 194 | 223 | 15 | 31 | 18 | 47 | 64 | 80 | 126 | 114 |
132 | 116 | 100 | 179 | 163 | 150 | 196 | 183 | 212 | 4 | 35 | 21 | 54 | 68 | 82 |
70 | 89 | 133 | 120 | 91 | 168 | 152 | 139 | 200 | 186 | 219 | 8 | 37 | 27 | 56 |
28 | 60 | 61 | 78 | 122 | 109 | 95 | 171 | 159 | 143 | 202 | 192 | 221 | 10 | 44 |