When I was poking PE many many years ago, one approach I took was "make a brute-force solver, feed it small inputs, see if there is an easy way to reason myself

When I was poking PE many many years ago, one approach I took was "make a brute-force solver, feed it small inputs, see if there is an easy way to reason myself to a closed form". This sometimes involved looking sequences up in OEIS, sometimes the closed for was obvious from the sequence, and sometimes I used differentials to find it.