If we assume a linear relationship of the type a(n)=Aa(n-1)+Ba(n-2)+Ca(n-3) where A, B, C are constants and a(n) represents the nth term for n>0, the formula would be a(n)=(12/71)a(n-1)-(321/71)a(n-2)+(1931/71)a(n-3) when a₁=1, a₂=2, a₃=5. The iterative formula gives a₄=19, a₅=35 and a₆=56. The values of A, B, C were found by solving a system of simultaneous equations. a₇ under this formula is 26126/71.
However, the formula looks messy, so it’s not likely to be the correct answer in this case, and it would be complicated to use it for finding the nth term.