A set of numbers is defined as a1=1, a2=2, a3=3, and a number n belongs to this set if it can be written as a unique sum of three distinct members of this set e.g. a4=6, a5=9, a6=10, a7=11, a8=12 but 13, 14, 15, 16, 17 do not belong to this set. Is this set of numbers finite or infinite? Prove your claim.

_____________________

I've been trying to solve this question by contradiction. So I assume that the set is finite. I have no idea how to proceed. can anyone give me a hint?