A261752 Minimum number of knights on an n X n chessboard such that every square is attacked.

6, 7, 8, 10, 14, 18, 22, 25, 28, 32, 36, 43, 48, 54, 58, 66, 70, 78, 84, 91, 98, 107, 112, 123, 128, 139, 146, 156, 164

Offset: 4

Author

Matthew Conroy, Aug 31 2015

Keywords

• nonn
• more

Comments

Total domination number of n X n knight graph.

Distinct from A006075 since here all squares must be attacked, whereas, in A006075, all squares are either attacked or occupied.

a(34) = 182, a(36) = 202, a(38) = 224. - Andy Huchala, Jun 04 2021

Examples

			An example for the 4 X 4 case:
  ....
  .NNN
  .N..
  NN..
and for the 5 x 5 case:
  .....
  ..N..
  .NN..
  NNN..
  N....
		

Links

• Matthew Conroy, Examples of minimum knight arrangements, n = 4 through n = 14
• Andy Huchala, Python program
• Giovanni Resta, Examples of minimum knight arrangements, from n = 15 to n = 18
• Andy Huchala, Examples of minimum knight arrangements, from n = 25 to n = 34
• Eric Weisstein's World of Mathematics, Knight Graph
• Eric Weisstein's World of Mathematics, Total Domination Number

Crossrefs

Cf. A006075.

Extensions

a(15)-a(18) from Giovanni Resta, Aug 31 2015

a(19)-a(26) from Andy Huchala, Oct 16 2017

a(27)-a(30) from Andy Huchala, Oct 18 2017

a(31)-a(32) from Andy Huchala, Jun 04 2021