Some calculations for the non attacking queens problem using a graph-theoretic node-contraction algorithm (aka Node-Kayles).
To run and build (with release):
bash release.sh
./target/release/node-kayles [args]
The new terms for the following OEIS sequences are shown below, along with steps to reproduce. All bolded and italicized sequence terms are new/novel results that were previously unknown.
Non-Attacking Queens Sequence (OEIS A344227)
bash release.sh
bash scripts/queens.sh
Sequence (where the first term is a 0x0 chessboard): 0, 1, 1, 2, 1, 3, 1, 2, 3, 1, 0, 1, 0, 1
A naive Haskell implementation can be found at haskell-impls/queens.hs).
Generalized Petersen Sequence (OEIS A316533)
Note: this script will skip every other term since it has been proven that for all even values, the Sprague-Grundy value is 0.
bash release.sh
bash scripts/petersen_n_2.sh
Sequence (where the first term is P(5,2)): 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0
3xN Lattice Sequence (OEIS A316632)
bash release.sh
bash scripts/lattice_3_n.sh
Sequence (where the first term is the 3x1 lattice): 2, 1, 1, 0, 3, 3, 2, 2, 2, 3, 3, 5, 2, 4, 1, 3
A naive Haskell implementation can be found at haskell-impls/lattice.hs).
This project is licensed under GPL-3.0-only.
Pull requests, feedback, and contributions are always welcome.