A352623 a(n) is the maximum number k of queens that can be placed on an n X n chessboard such that, for each number j in 0..k-1, there is a queen attacking exactly j unoccupied squares.

0, 1, 0, 5, 8, 11, 14, 18, 22

Offset

0,4

Comments

On the 6 X 6 board in the illustration (see Example), each square containing a number is occupied by a queen, and the number in that square is the number of unoccupied squares attacked by that queen. (Each square with no number is unoccupied.)

Solvers:

a(4) = 8 by Rodolfo Kurchan

a(5) = 11 by Gustavo Piñeiro

a(6) = 14 by Antonio Misericordia

a(7) = 18 by Antonio Misericordia

a(8) = 22 by Giorgio Vecchi

Links

Table of n, a(n) for n=0..8.

Rodolfo Kurchan, Chess Puzzle Fun 5 Uneven Attacks

Example

Solution illustrating a(6) = 14 by Antonio Misericordia:
  +---+---+---+---+---+---+
  | 2 | 7 |   | 5 | 4 | 0 |
  +---+---+---+---+---+---+
  | 10|   |   |   | 6 | 1 |
  +---+---+---+---+---+---+
  |   |   |   | 11|   | 3 |
  +---+---+---+---+---+---+
  |   |   |   | 13|   | 8 |
  +---+---+---+---+---+---+
  |   |   |   |   |   |   |
  +---+---+---+---+---+---+
  |   |   | 12|   | 9 |   |
  +---+---+---+---+---+---+

Crossrefs

Cf. A186238.

Sequence in context: A063247 A184928 A186238 * A314389 A363889 A118520

Adjacent sequences: A352620 A352621 A352622 * A352624 A352625 A352626

Keyword

nonn,more

Author

Rodolfo Kurchan, Mar 24 2022

Status

approved