A261752 - OEIS

%I #38 Jun 04 2021 22:44:33

%S 6,7,8,10,14,18,22,25,28,32,36,43,48,54,58,66,70,78,84,91,98,107,112,

%T 123,128,139,146,156,164

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

%C Total domination number of n X n knight graph.

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

%C a(34) = 182, a(36) = 202, a(38) = 224. - _Andy Huchala_, Jun 04 2021

%H Matthew Conroy, <a href="/A261752/a261752.png">Examples of minimum knight arrangements, n = 4 through n = 14</a>

%H Andy Huchala, <a href="/A261752/a261752.py3.txt">Python program</a>

%H Giovanni Resta, <a href="/A261752/a261752.pdf">Examples of minimum knight arrangements, from n = 15 to n = 18</a>

%H Andy Huchala, <a href="/A261752/a261752_1.pdf">Examples of minimum knight arrangements, from n = 25 to n = 34</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotalDominationNumber.html">Total Domination Number</a>

%e An example for the 4 X 4 case:

%e   ....

%e   .NNN

%e   .N..

%e   NN..

%e and for the 5 x 5 case:

%e   .....

%e   ..N..

%e   .NN..

%e   NNN..

%e   N....

%Y Cf. A006075.

%K nonn,more

%O 4,1

%A _Matthew Conroy_, Aug 31 2015

%E a(15)-a(18) from _Giovanni Resta_, Aug 31 2015

%E a(19)-a(26) from _Andy Huchala_, Oct 16 2017

%E a(27)-a(30) from _Andy Huchala_, Oct 18 2017

%E a(31)-a(32) from _Andy Huchala_, Jun 04 2021