A356404 The number of closed routes of the chess knight, different in shape, consisting of 2 * n jumps on a checkered field without repeating cells of the route.

1, 3, 25, 480, 11997, 350275, 10780478

Offset: 1

Author

Nicolay Avilov, Aug 05 2022

Keywords

• nonn
• walk
• hard
• more

Comments

Various closed routes of a chess knight on an unbounded checkered field are considered. The closed route of the chess knight means that with the last jump the chess knight returns to its original cell. A chess knight cannot jump into the same square twice.

The first three members of the sequence were found by me manually, the remaining members were found by Talmon Silver using a computer program.

Examples

			a(1)=1, since the only closed route for n=1 can be considered two jumps of a chess knight from any cell and back;
a(2)=3 because the chess knight has 3 closed routes consisting of 4 jumps. We list them in the coordinate plane Oxy:
   1st route: (0;0), (1;2), (3;3), (2;1), (0;0);
   2nd route: (0;1), (1;3), (3;2), (2;0), (0;1);
   3rd route: (0;1), (2;2), (4;1), (2;0), (0;1).
		

Links

• Nicolay Avilov, Problem 1820. Routes of the chess knight (in Russian).
• Talmon Silver, Nikoly Avilov's picture for a(3)

Crossrefs

Cf. A323131, A323559.