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

1,2

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.

References

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

Links

Table of n, a(n) for n=1..16.

Andy Huchala, Python program.

Example

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

Crossrefs

Cf. A006075, A279402.

Sequence in context: A269857 A269847 A358522 * A245705 A075164 A240827

Adjacent sequences: A279404 A279405 A279406 * A279408 A279409 A279410

Keyword

nonn,hard,more

Author

Andrey Zabolotskiy, Dec 12 2016

Extensions

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

Status

approved