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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. 3
1, 3, 25, 480, 11997, 350275, 10780478 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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.
LINKS
Nicolay Avilov, Problem 1820. Routes of the chess knight (in Russian).
EXAMPLE
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).
CROSSREFS
Sequence in context: A223076 A336804 A272482 * A366778 A136173 A243440
KEYWORD
nonn,walk,hard,more
AUTHOR
Nicolay Avilov, Aug 05 2022
STATUS
approved

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Last modified September 11 23:02 EDT 2024. Contains 375842 sequences. (Running on oeis4.)