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

4,1

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

Links

Table of n, a(n) for n=4..32.

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

Example

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

Crossrefs

Cf. A006075.

Sequence in context: A031237 A031314 A209723 * A248902 A295668 A274556

Adjacent sequences: A261749 A261750 A261751 * A261753 A261754 A261755

Keyword

nonn,more

Author

Matthew Conroy, Aug 31 2015

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

Status

approved