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A261752 Minimum number of knights on an n X n chessboard such that every square is attacked. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 10:32 EST 2022. Contains 358556 sequences. (Running on oeis4.)