A098604 Triangle T(n,k) read by rows, for 1 <= k <= n: minimal number of knights needed to cover a k X n board.

1, 2, 4, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 6, 4, 4, 4, 6, 8, 7, 6, 6, 6, 7, 8, 10, 8, 8, 8, 8, 8, 8, 11, 12, 9, 8, 8, 8, 8, 10, 12, 13, 14, 10, 8, 8, 8, 9, 12, 14, 14, 15, 16, 11, 8, 8, 8, 10, 12, 15, 16, 17, 19, 21, 12, 8, 8, 8, 10, 12, 16, 16, 18, 20, 22, 24, 13, 10, 10, 10, 12, 14

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• nice

Comments

How many knights are needed to occupy or attack every square of a k X n board?

I do not know how many of these numbers have been proved to be optimal. - N. J. A. Sloane, Nov 08 2004

Examples

			Triangle (with rows n >= 1 and columns k >= 1) begins as follows:
  1
  2 4
  3 4 4
  4 4 4 4
  5 4 4 4 5
  6 4 4 4 6 8
  7 6 6 6 7 8 10
  ...
		

Links

• Lee Morgenstern, Knight Domination.
• Frank Rubin, Knight coverings for large chessboards, 2000.
• Eric Weisstein's World of Mathematics, Knights Problem.

Crossrefs

See A006075 for the n X n case (the main diagonal). A006076 gives number of ways to cover an n X n board using the minimal number of knights.

Extensions

Morgenstern's table extends a long way beyond what is shown here.