%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