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Number of paths for a Racetrack car (using Moore neighborhood) with initial velocity zero, going from one corner to the diagonally opposite corner on an n X n grid, such that all positions are visited exactly once.
2

%I #6 Feb 04 2022 14:41:12

%S 1,0,6,2,9436

%N Number of paths for a Racetrack car (using Moore neighborhood) with initial velocity zero, going from one corner to the diagonally opposite corner on an n X n grid, such that all positions are visited exactly once.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Racetrack_(game)">Racetrack</a>

%e For n = 4 the following path and its reflection in the diagonal are the only solutions, so a(4) = 2.

%e _ _

%e | | |_

%e |_ \ |

%e _| |_|

%Y Main diagonal of A351110.

%Y Cf. A272445, A351041, A351107.

%K nonn,more

%O 1,3

%A _Pontus von Brömssen_, Feb 01 2022