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.

3, 5, 12, 12, 16, 27, 27, 33, 48, 48, 56, 75, 75, 85, 108, 108, 120, 147, 147, 161, 192, 192, 208, 243, 243, 261, 300, 300, 320, 363, 363, 385, 432, 432, 456, 507, 507, 533, 588, 588, 616, 675, 675, 705, 768, 768, 800, 867, 867, 901, 972, 972, 1008, 1083, 1083

Offset: 2

Author

Matthew Scroggs, Jan 02 2025

Keywords

• nonn

Comments

At most one king can be placed on each square.

Examples

			For a 3 by 3 chessboard, the five kings could be placed like this:
   oko
   kkk
   oko
For a 4 by 4 chessboard, the kings could be placed like this:
   okko
   kkkk
   kkkk
   okko
where o is an empty square and k is a king.
		

Links

• Dominic McCarty, Table of n, a(n) for n = 2..100
• Matthew Scroggs, Python code to compute A379759
• Dominic McCarty, Illustration of a(n) for n = 2...100
• Dominic McCarty, Java program for A379759

Crossrefs

Cf. A075561, A379726, A379766.

Formula

It appears that a(3n+1) = a(3n+2) - Dominic McCarty, Jan 17 2025

Extensions

a(9)-a(100) from Dominic McCarty, Jan 17 2025