# Hamiltonian paths and cycles of rook graph on $n\times2$ chessboard

According to OEIS, there are closed form for directed Hamiltonian paths (A096121) and Hamiltonian cycles (A276356) of rook graph on $$n\times2$$ chessboard. Are there papers which include proof of those closed forms? Are there closed forms for $$n\times m$$ (A269565, A269562) with $$m>2$$?

• At least for oeis.org/A276356, the comments on the OEIS sequence appear to contain a proof. – Misha Lavrov Mar 9 at 16:02
• @MishaLavrov, thank you for comment! Given proof is not clear to me. – user514787 Mar 9 at 16:24