cp's OEIS Frontend

A375116 Maximum number of squares covered (i.e., attacked) by 3 independent (i.e., nonattacking) queens on an n X n chessboard.

%I A375116 #38 Oct 05 2024 14:00:31
%S A375116 16,25,35,45,55,66,77,88,101,112,125,136,149,160,173,184,197,208,221,
%T A375116 232,245,256,269,280,293,304,317,328,341,352,365,376,389,400,413,424,
%U A375116 437,448,461,472,485,496,509,520,533,544,557,568,581,592,605,616,629,640,653,664,677
%N A375116 Maximum number of squares covered (i.e., attacked) by 3 independent (i.e., nonattacking) queens on an n X n chessboard.
%C A375116 It is not possible to place 3 independent queens on a 1 X 1 or 2 X 2 or 3 X 3 board.
%C A375116 There is a related sequence of 'uncovered' squares i.e., n^2 - a(n).
%C A375116 There is another sequence denoting the potency of the new queen a(n) - A374933(n).
%F A375116 a(n) = 12*n - 43 - (n mod 2) for n >= 10.
%e A375116 4 X 4 complete coverage with 3 queens
%e A375116   x x x x
%e A375116   x Q x x
%e A375116   x x x Q
%e A375116   Q x x x
%e A375116 5 X 5 complete coverage with 3 queens
%e A375116   Q x x x x
%e A375116   x x x x x
%e A375116   x x x Q x
%e A375116   x x x x x
%e A375116   x x Q x x
%e A375116 6 X 6 incomplete 1 o/s
%e A375116   x x x x o x
%e A375116   Q x x x x x
%e A375116   x x x x x Q
%e A375116   x x x x x x
%e A375116   x x Q x x x
%e A375116   x x x x x x
%e A375116 6 X 6 coverage complete but NOT independent
%e A375116   Q x x x x x
%e A375116   x x x x x x
%e A375116   x x x x q x
%e A375116   x x x x x x
%e A375116   x x q x x x
%e A375116   x x x x x x
%e A375116 7 X 7 best leaves 4 o/s  (same layout as 6 X 6 with extra row and column)
%e A375116 There are alternative layouts - how many is not identified.
%e A375116   x x x x o x x
%e A375116   Q x x x x x x
%e A375116   x x x x x Q x
%e A375116   x x x x x x x
%e A375116   x x Q x x x x
%e A375116   x x x x x x o
%e A375116   x x x o x x o
%Y A375116 Column 3 of A376732.
%Y A375116 Cf. A047461 (for one queen), A374933 (for two queens), A374934, A374935, A374936.
%K A375116 nonn
%O A375116 4,1
%A A375116 _John King_, Jul 30 2024
%E A375116 a(6)-a(8) corrected by _John King_, Sep 17 2024
%E A375116 a(9) corrected using data from _Mia Muessig_ by _Andrew Howroyd_, Oct 05 2024