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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. 1
0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14 (list; graph; refs; listen; history; text; internal format)
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 co-exist 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

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Last modified May 21 00:36 EDT 2022. Contains 353886 sequences. (Running on oeis4.)