I arrived at the same solutions as Charlie with a program. It's pretty simple so show that if any of the first 3 terms are too large then A(6) will exceed 144.
An attempt at solving this analytically with algebra leads quickly to a brick wall of a formula: a 5th degree polynomial Diophantine equation in three variables with 10 terms. I won't even type it out.
It is quadratic in A(1) but cubic in A(2) and quartic in A(3).
Posted by Jer
on 2016-07-22 11:16:48