A361453 Number of colorings of the n X n knight graph up to permutation of the colors.

1, 15, 4141, 450288795, 50602429743064097, 12123635532529660182357354372

Offset: 1

Author

Andrew Howroyd, Mar 13 2023

Keywords

• nonn
• more

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.

Examples

			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).
		

Links

• Eric Weisstein's World of Mathematics, Knight Graph.
• Eric Weisstein's World of Mathematics, Vertex Coloring.

Crossrefs

Main diagonal of A208001.

Cf. A000110, A207863 (grid graph), A289136 (king), A295178.

Formula

a(n) <= A000110(n^2).