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Maximum number of squares covered (i.e., attacked) by 6 independent (i.e., nonattacking) queens on an n X n chessboard.
4

%I #42 Oct 30 2024 08:07:26

%S 36,49,64,81,100,121,142,165,186,209,231,255,277

%N Maximum number of squares covered (i.e., attacked) by 6 independent (i.e., nonattacking) queens on an n X n chessboard.

%e Example for 12 X 12: There are 2 cells marked 'o' or uncovered thus a(12) = 12 * 12 - 2 = 142.

%e x x x x x x x x x x x Q

%e x x x x x x x x x x x x

%e x x x x x x x x x x x x

%e x x x Q x x x x x x x x

%e x x x x x Q x x x x x x

%e x x x x x x x Q x x x x

%e x x x x Q x x x x x x x

%e x x x x x x Q x x x x x

%e o x x x x x x x x x x x

%e x x x x x x x x x x x x

%e x x x x x x x x x x x x

%e x x x x x x x x o x x x

%e From _Christian Sievers_, Sep 08 2024: (Start)

%e Example for 14 X 14 with 186 attacked squares (unattacked ones marked with "+"):

%e . . Q . . . . . . . . . . .

%e . . . . . . . . . Q . . . .

%e . . . . . . . . . . . . . +

%e . + . . . . . . . . . . . .

%e . . . Q . . . . . . . . . .

%e . . . . . . . . . . . . . .

%e . . . . . . . . . . . . . .

%e . . . . . . . . . . . . Q .

%e . + . . . . . . . . . . . .

%e . . . . . . . . . . . . . +

%e . . . . . . Q . . . . . . .

%e . + . . + . . . . . . + . .

%e . . . . . + . . . . + . . +

%e Q . . . . . . . . . . . . .

%e (End)

%Y Column 6 of A376732.

%Y Cf. A075324, A047461, A374933, A375116, A374933, A374934, A374935, A374937, A374938.

%K nonn,more

%O 6,1

%A _John King_, Aug 08 2024

%E a(14) corrected and a(15) confirmed by _Christian Sievers_, Sep 08 2024

%E a(16)-a(18) added using data from _Mia Muessig_ by _Andrew Howroyd_, Oct 05 2024