A103315 Number of minimum dominating sets for the n X n knight graph.

1, 1, 8, 9, 47, 127, 10, 2, 2, 4, 800, 2, 152, 4, 504, 2, 212, 19562

Offset

1,3

Comments

In other words, as made explicit in the old name: Sequence A006075 gives minimum number of knights needed to cover an n X n board (i.e., the domination number of the n X n knight graph). This sequence (A103315) gives total number of solutions using A006075(n) knights (compare A006076).

Links

Table of n, a(n) for n=1..18.

Lee Morgenstern, Knight Domination.

Frank Rubin, Knight coverings for large chessboards, 2000.

Eric Weisstein's World of Mathematics, Knight Graph

Eric Weisstein's World of Mathematics, Minimum Dominating Set

Crossrefs

Cf. A006075 (domination number of the n X n knight graph).

Cf. A006076 (inequivalent number of minimum dominating sets).

Cf. A098604.

Sequence in context: A048068 A037957 A165239 * A175931 A270013 A341526

Adjacent sequences: A103312 A103313 A103314 * A103316 A103317 A103318

Keyword

nonn,more

Author

N. J. A. Sloane, Mar 20 2005, following a suggestion from Lee Morgenstern.

Extensions

New name from Eric W. Weisstein, Sep 06 2021

Status

approved