

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
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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



