Each number from 1 to 441 must pair with two other valid numbers to add to two of target sums 321, 442 or 763, as the sequence goes to a number and then away from it again. For example, 13 would pair with 308, 429 and 750 to form the target sums. 750 is outside of the range of numbers in the sequence, so therefore 308 and 429 must be either side of 13 in the sequence. This is true for every number except for the numbers at the very ends of the sequence, which can only for a valid pair adding to ONE of the target sums. These are 321, which would pair with 0, 121 and 442 to form the target sums, and only 121 is in the range 1-441. At the other end of the sequence will be 221, which pairs with 100, 221 or 542. 542 is outside of the range, and 221 is the same number again, so 100 must be adjacent to 221. So 221 and 321 are at the ends of the sequence.

It's not obvious, and I won’t go into the reasons here, but at the exact middle of the sequence will be the average of those two end numbers, 271.