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A361453
Number of colorings of the n X n knight graph up to permutation of the colors.
1
1, 15, 4141, 450288795, 50602429743064097, 12123635532529660182357354372
OFFSET
1,2
COMMENTS
Any number of colors may be used.
Equivalently, a(n) is the number of stable partitions of the n X n knight graph. A stable partition is a partition of the vertices into sets so that no two vertices in a set are adjacent in the graph.
LINKS
Eric Weisstein's World of Mathematics, Knight Graph.
Eric Weisstein's World of Mathematics, Vertex Coloring.
FORMULA
a(n) <= A000110(n^2).
EXAMPLE
a(2) = 15 = A000110(4) because the graph has no edges and so there are no restrictions on how the vertices may be colored (or equivalently the vertices partitioned into sets).
CROSSREFS
Main diagonal of A208001.
Cf. A000110, A207863 (grid graph), A289136 (king), A295178.
Sequence in context: A208469 A070907 A208053 * A079919 A027513 A287037
KEYWORD
nonn,more
AUTHOR
Andrew Howroyd, Mar 13 2023
STATUS
approved