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A275815 Maximum total number of possible moves that any number of queens of the same color can make on an n X n chessboard. 4

%I

%S 0,4,17,40,76

%N Maximum total number of possible moves that any number of queens of the same color can make on an n X n chessboard.

%H Peter Kagey, <a href="/A275815/a275815.pdf">Examples for 1 <= n <= 5</a>.

%F Conjecture: a(n) = 8(n-2)^2 for n >= 6. - _Alec Jones_, Nov 16 2016

%F Lim_{n->oo} a(n)/n^2 = 8. Putting queens on the 4n-4 border locations shows that a(n) >= 8(n-2)^2. On the other hand, a(n) <= 8n^2 since each location is in the path of at most 8 queens. - _Chai Wah Wu_, Nov 19 2016

%e The following 3 X 3 chessboard illustrates a(3) = 17:

%e +---+---+---+

%e 3| Q | | Q |

%e +---+---+---+

%e 2| Q | | |

%e +---+---+---+

%e 1| | Q | |

%e +---+---+---+

%e A B C

%e The queen at A3 has three moves, the queen at A2 has four moves, and the queens at B1 and C3 each have five moves.

%Y Cf. A278211, A278212, A278214.

%K nonn,more

%O 1,2

%A _Peter Kagey_, Nov 14 2016

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Last modified June 5 16:19 EDT 2020. Contains 334852 sequences. (Running on oeis4.)