A362601 Domination number for pawns' graph P(n).

1, 2, 5, 8, 12, 16, 23, 28, 33, 44, 49, 56, 70, 78, 85, 104, 111, 120, 141, 152, 161, 188, 197, 208, 237, 250, 261, 296, 307, 320, 357, 372, 385, 428, 441, 456, 501, 518, 533, 584

Offset: 1

Author

Rodolfo Kurchan, Jun 18 2023

Keywords

• nonn
• more

Comments

Minimum number of white pawns needed to occupy or attack all squares of an n X n chessboard.

Solutions for boards of sizes 1 to 8, 10, 14, 15 from Rodolfo Kurchan.

Solutions for boards of sizes 9, 11, 12, 14 to 18, 20 to 24 from Michael Steinau.

Solution for boards of size 13 and 25 to 40 from M. Achterberg.

Examples

			a(8) = 28 white pawns occupying or attacking all squares of a standard chessboard:
  . . . . . . . .
  . P P P P P P .
  . P . . . . P .
  . P . P P . P .
  . P . . . . P .
  . P . P P . P .
  . P . . . . P .
  P P P P P P P P
		

Links

• M. Achterberg, Illustration for a(13) = 70.
• Rodolfo Kurchan, Board domination problem, Chess Puzzle Fun 6, April 2023.

Crossrefs

Cf. A075458.