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A379759 Minimum number of kings that must be placed on an n X n chessboard such that each square is attacked or occupied by at least three kings.

%I A379759 #30 Jan 18 2025 09:33:53
%S A379759 3,5,12,12,16,27,27,33,48,48,56,75,75,85,108,108,120,147,147,161,192,
%T A379759 192,208,243,243,261,300,300,320,363,363,385,432,432,456,507,507,533,
%U A379759 588,588,616,675,675,705,768,768,800,867,867,901,972,972,1008,1083,1083
%N A379759 Minimum number of kings that must be placed on an n X n chessboard such that each square is attacked or occupied by at least three kings.
%C A379759 At most one king can be placed on each square.
%H A379759 Dominic McCarty, <a href="/A379759/b379759.txt">Table of n, a(n) for n = 2..100</a>
%H A379759 Matthew Scroggs, <a href="https://github.com/mscroggs/oeis/blob/main/a379759.py">Python code to compute A379759</a>
%H A379759 Dominic McCarty, <a href="/A379759/a379759_1.txt">Illustration of a(n) for n = 2...100</a>
%H A379759 Dominic McCarty, <a href="/A379759/a379759_2.txt">Java program for A379759</a>
%F A379759 It appears that a(3n+1) = a(3n+2) - _Dominic McCarty_, Jan 17 2025
%e A379759 For a 3 by 3 chessboard, the five kings could be placed like this:
%e A379759    oko
%e A379759    kkk
%e A379759    oko
%e A379759 For a 4 by 4 chessboard, the kings could be placed like this:
%e A379759    okko
%e A379759    kkkk
%e A379759    kkkk
%e A379759    okko
%e A379759 where o is an empty square and k is a king.
%Y A379759 Cf. A075561, A379726, A379766.
%K A379759 nonn
%O A379759 2,1
%A A379759 _Matthew Scroggs_, Jan 02 2025
%E A379759 a(9)-a(100) from _Dominic McCarty_, Jan 17 2025