Donald Knuth comments in one of his papers on the key role of the use of computers in making his paper possible.

D. E. Knuth, A class of projective planes. Transactions of the American Mathematical Society 115 (1965) 541–549.

Basically what happened was that Knuth used a computer to study an example and once he saw how that example worked he was able to see what was going on in general.

This is a common way that "experimental" mathematics can work. Doing experiments can lead to examples that provide the proof of how some general construction can be implemented.