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

2,1

Comments

At most one king can be placed on each square.

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

Formula

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

Example

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.

Crossrefs

Cf. A075561, A379726, A379766.

Sequence in context: A361111 A361322 A037221 * A182537 A259309 A212061

Adjacent sequences: A379755 A379756 A379758 * A379760 A379761 A379762

Keyword

nonn

Author

Matthew Scroggs, Jan 02 2025

Extensions

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

Status

approved