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Patterns in a table

This is part of a table of values of 3S2 + T2. Values of S are down the left-hand side and values of T are along the top. Values in the middle show the evaluation of the expression 3S2 + T2 using the values of S and T from the corresponding rows and columns. Expand the table to larger values of S and T and investigate any patterns you can find.

  T
1 2 3 4 5 6 7 8 9 10 11 12 13
S 1 4 7 12 19 28 39 52 67 84 103 124 147 172
2 13 16 21 28 37 48 61 76 93 112 133 156 181
3 28 31 36 43 52 63 76 91 108 127 148 171 196
4 49 52 57 64 73 84 97 112 129 148 169 192 217
5 76 79 84 91 100 111 124 139 156 175 196 219 244
6 109 112 117 124 133 144 157 172 189 208 229 252 277
7 148 151 156 163 172 183 196 211 228 247 268 291 316


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