A279407 Domination number for knight graph on an n X n toroidal board.

1, 2, 3, 4, 5, 6, 9, 8, 12, 15, 18, 21, 25, 28, 33, 32

Offset: 1

Author

Andrey Zabolotskiy, Dec 12 2016

Keywords

• nonn
• hard
• more

Comments

That is, the minimal number of knights needed to cover an n X n toroidal chessboard so that every square either has a knight on it, or is under attack by a knight, or both.

Examples

			For an 8 X 8 board, the solution is:
  N . . . . . . N
  . . . . . . . .
  . . N . . N . .
  . . . . . . . .
  . . . N N . . .
  . . . . . . . .
  . N . . . . N .
  . . . . . . . .
		

References

• John J. Watkins, Across the Board: The Mathematics of Chessboard Problem, Princeton University Press, 2004, pages 140-144.

Links

• Andy Huchala, Python program.

Crossrefs

Cf. A006075, A279402.

Extensions

a(9)-a(16) from Andy Huchala, Mar 03 2024