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A328283 The maximum number m such that m white, m black and m red queens can coexist on an n X n chessboard without attacking each other.

%I A328283 #27 Jan 27 2023 17:21:53
%S A328283 0,0,0,1,1,2,3,4,5,7,8,10,12,14
%N A328283 The maximum number m such that m white, m black and m red queens can coexist on an n X n chessboard without attacking each other.
%C A328283 This is the peaceable queens problem (A250000) for 3 players.
%C A328283 For n >= 11, it seems that a(n) is simply 2n - 14. However this turns out to be false as a(18) >= 23.
%C A328283 In the limit of large n, _Arthur O'Dwyer_ (see links) showed that the optimal value is lower bounded by 0.0718*n^2. All currently known best solutions follow this formula (when rounded down). - _M. A. Achterberg_, Dec 01 2022
%H A328283 M. A. Achterberg, <a href="/A328283/a328283_2.txt">Best known solutions for n <= 30</a>, Dec 01 2022.
%H A328283 Dmitry Kamenetsky, <a href="/A328283/a328283_1.txt">Best known solutions for n <= 24</a>.
%H A328283 Arthur O'Dwyer, <a href="https://quuxplusone.github.io/blog/2019/01/24/discrete-peaceful-encampments">Discrete Peaceful Encampments</a>, 2019.
%H A328283 Arthur O'Dwyer, <a href="https://puzzling.stackexchange.com/questions/78801/discrete-peaceful-encampments-player-3-has-entered-the-game">Discrete Peaceful Encampments: Player 3 has entered the game!</a>, Puzzling StackExchange, 2019.
%H A328283 Arthur O'Dwyer, <a href="https://quuxplusone.github.io/blog/2019/01/21/peaceful-encampments-round-2">Peaceful Encampments, round 2</a>, 2019.
%e A328283 a(8) = 4, because 4 queens of each color can co-exist without attacking queens of another color. Note that in this case both red (6) and white (5) have more than 4 queens.
%e A328283 + - - - - - - - - +
%e A328283 | R . R . R . . . |
%e A328283 | R . . . . . . . |
%e A328283 | . . . . . W . W |
%e A328283 | R . R . . . . . |
%e A328283 | . . . . . W . W |
%e A328283 | . B . B . . . . |
%e A328283 | . . . . . . . W |
%e A328283 | . B . B . . . . |
%e A328283 + - - - - - - - - +
%Y A328283 Cf. A250000.
%K A328283 nonn,more,hard
%O A328283 1,6
%A A328283 _Dmitry Kamenetsky_, Oct 11 2019