cp's OEIS Frontend

A308632 Largest aggressor for the maximum number of peaceable coexisting queens as given in A250000.

%I A308632 #35 Feb 06 2022 14:59:23
%S A308632 0,0,2,3,4,6,7,10,12,15,19
%N A308632 Largest aggressor for the maximum number of peaceable coexisting queens as given in A250000.
%C A308632 Sequence A250000 is the maximum number m such that m white queens and m black queens can coexist on an n X n chessboard without attacking each other. However, one of the players can have more than m queens, being a bigger 'aggressor' in peaceful times. The current sequence lists the largest aggressors with k queens when the opponent has m queens for an n X n chessboard (from A250000).
%C A308632 The idea and name of the sequence was first mentioned by _Bob Selcoe_ on May 29 2019 in the comment section of A250000.
%C A308632 The sequence was initially generated by _Roy van Rijn_ using a SAT solver and is optimal for n=1 to n=11 (as of June 12 2019).
%C A308632 _Bob Selcoe_ has shown it is possible to construct a 15 X 15 board with 32 queens of one color and 34 of another but this hasn't yet been proved to be optimal.
%C A308632 Many of these values have already been obtained by Stephen Ainley in 1977 (see links).
%C A308632 Conjecture: a(n) - A250000(n) <= 2 for all n. - _Dmitry Kamenetsky_, Oct 14 2019
%H A308632 Stephen Ainley, <a href="/A250000/a250000_6.png">Mathematical Puzzles</a>, London: G Bell & Sons, 1977. [Annotated scan of a portion of page 32]
%H A308632 Dmitry Kamenetsky, <a href="/A308632/a308632_1.txt">Best known solutions for 12 <= n <= 30</a>.
%F A308632 a(n) >= A250000(n).
%e A308632 Examples (omitted cases where the largest aggressor is equal to A250000):
%e A308632   n=1: white queens 0, black queens 0
%e A308632   n=2: white queens 0, black queens 0
%e A308632   n=3: white queens 1, black queens 2
%e A308632   n=4: white queens 2, black queens 3
%e A308632   +---------+
%e A308632   | . W . W |
%e A308632   | . . . . |
%e A308632   | B . B . |
%e A308632   | . . B . |
%e A308632   +---------+
%e A308632   n=5: white queens 4, black queens 4
%e A308632   n=6: white queens 5, black queens 6
%e A308632   +-------------+
%e A308632   | . W . . . . |
%e A308632   | W . W . . . |
%e A308632   | . . . . B B |
%e A308632   | . . . B . B |
%e A308632   | W W . . . . |
%e A308632   | . . . B . B |
%e A308632   +-------------+
%e A308632   n=7: white queens 7, black queens 7
%e A308632   n=8: white queens 9, black queens 10
%e A308632   +-----------------+
%e A308632   | . . . B B B . . |
%e A308632   | W W . . . . . . |
%e A308632   | . . . B . . . B |
%e A308632   | . . . . . . B B |
%e A308632   | . . . . . B B B |
%e A308632   | . W W . . . . . |
%e A308632   | W W W . . . . . |
%e A308632   | W W . . . . . . |
%e A308632   +-----------------+
%e A308632   n=9: white queens 12, black queens 12
%e A308632   n=10: white queens 14, black queens 15
%e A308632   +---------------------+
%e A308632   | . . B B . . . . B B |
%e A308632   | . . B B . . . B B B |
%e A308632   | . . B . . . . B B B |
%e A308632   | . . . . . . . B B . |
%e A308632   | . W . . . . . . . . |
%e A308632   | W W . . . . . . . . |
%e A308632   | W W . . . . . . . . |
%e A308632   | W . . . . W W . . . |
%e A308632   | . . . . W W W . . . |
%e A308632   | . . . . W W W . . . |
%e A308632   +---------------------+
%e A308632   n=11: white queens 17, black queens 19
%e A308632   +-----------------------+
%e A308632   | W . W . . . . . W . W |
%e A308632   | . . . . B B B . . . . |
%e A308632   | W . W . . . . . W . W |
%e A308632   | . . . . B . B . . . . |
%e A308632   | . B . . . B . B . B . |
%e A308632   | . B . . B . B . . B . |
%e A308632   | . B . . . B . B . B . |
%e A308632   | . . . . B . B . . . . |
%e A308632   | W . W . . . . . W . W |
%e A308632   | . . . W . . . . . . . |
%e A308632   | W . W . . . . . W . W |
%e A308632   +-----------------------+
%Y A308632 Cf. A250000.
%K A308632 nonn,hard,more
%O A308632 1,3
%A A308632 _Roy van Rijn_, Jun 12 2019