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.
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
KEYWORD
nonn,fini,full
AUTHOR
Alexios Zavras, Mar 02 2021
STATUS
approved