cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A342151 #34 Mar 26 2021 12:48:02
%S A342151 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,
%T A342151 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
%N A342151 Maximum number of safe (i.e., not attacked) squares when placing n queens on a standard 8 X 8 chessboard.
%C A342151 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.
%e A342151 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:
%e A342151 .
%e A342151         Q Q Q . . . . .
%e A342151         . Q Q Q . . . .
%e A342151         . . . . . s s s
%e A342151         . . . . . . s s
%e A342151         . . . . . . . s
%e A342151         Q Q . . . . . .
%e A342151         . . . . s s . .
%e A342151         . . . . s s s .
%e A342151 .
%e A342151 This is in fact the "first" solution (when all possible ones are sorted), with the queens nearest the top-left corner.
%Y A342151 Cf. A001366, which answers the same question but on boards of different sizes and same number of queens.
%K A342151 nonn,fini,full
%O A342151 1,1
%A A342151 _Alexios Zavras_, Mar 02 2021