A342151 Maximum number of safe (i.e., not attacked) squares when placing n queens on a standard 8 X 8 chessboard.

42, 31, 25, 24, 17, 15, 13, 11, 10, 9, 8, 7, 7, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,1

Comments

On a standard chessboard, one can place from 1 to 64 queens. By arranging them in specific patterns, one can maximize the number of "safe" squares, i.e., squares that are not attacked by any queen.

Links

Table of n, a(n) for n=1..63.

Example

a(8)=11 because the maximum number of safe squares when 8 queens are placed on a regular 8 X 8 chessboard is 11. In the diagram below, each Q represents a queen and each s is a safe square:
.
        Q Q Q . . . . .
        . Q Q Q . . . .
        . . . . . s s s
        . . . . . . s s
        . . . . . . . s
        Q Q . . . . . .
        . . . . s s . .
        . . . . s s s .
.
This is in fact the "first" solution (when all possible ones are sorted), with the queens nearest the top-left corner.

Crossrefs

Cf. A001366, which answers the same question but on boards of different sizes and same number of queens.

Sequence in context: A053721 A195750 A331483 * A070723 A221213 A165863

Adjacent sequences: A342148 A342149 A342150 * A342152 A342153 A342154

Keyword

nonn,fini,full

Author

Alexios Zavras, Mar 02 2021

Status

approved