

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.


1



0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14
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OFFSET

1,6


COMMENTS

This is the peaceable queens problem (A250000) for 3 players.
For n >= 11, it seems that a(n) is simply 2n  14. However this turns out to be false as a(18) >= 23.


LINKS

Table of n, a(n) for n=1..14.
Dmitry Kamenetsky, Best known solutions for n <= 24.
Arthur O'Dwyer, Discrete Peaceful Encampments, 2019.
Arthur O'Dwyer, Discrete Peaceful Encampments: Player 3 has entered the game!, Puzzling StackExchange, 2019.


EXAMPLE

a(8) = 4, because 4 queens of each color can coexist without attacking queens of another color. Note that in this case red has more than 4 queens.
+         +
 . . W W . . . . 
 . . W W . . . . 
 . . . . . . R R 
 . . . . . . . R 
 . . . . R . . . 
 B B . . . . . . 
 B B . . . . . . 
 . . . . R R R R 
+         +


CROSSREFS

Cf. A250000.
Sequence in context: A062469 A340758 A238098 * A034156 A034157 A135675
Adjacent sequences: A328280 A328281 A328282 * A328284 A328285 A328286


KEYWORD

nonn,more,hard


AUTHOR

Dmitry Kamenetsky, Oct 11 2019


STATUS

approved



