Combinatorics, Algorithm, and Humanity
a lovely story on combinatorics problem, algorithm, and humanity.
the sequence is “Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of an n X n grid.” , sequence id A007764, see https://oeis.org/A007764
there isn't a closed form formula know so far. We have counted up to f.
This problem, seems to be spurred by a computer game named The Witness.
Buy at amazon
The Witness (2016 video game)