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 A278211 Maximum total number of possible moves that any number of rooks of the same color can make on an n X n chessboard. 4

%I

%S 0,4,12,28,48

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

%C a(n) <= A275815(n).

%H Peter Kagey, <a href="/A278211/a278211.pdf">Examples for 1 <= n <= 5</a>.

%F Lim_{n->oo} a(n)/n^2 = 4. Putting rooks on the 4n-8 border locations that are not corners shows that a(n) >= 4(n-2)^2 + 8. On the other hand, a(n) <= 4n^2 since each location is in the path of at most 4 rooks. - _Chai Wah Wu_, Nov 20 2016

%e The following 4 X 4 chessboard illustrates a(4) = 28:

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

%e 4| R | | | R |

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

%e 3| | | R | |

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

%e 2| | R | | |

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

%e 1| R | | | R |

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

%e A B C D

%e The rooks at B2 and C3 each have six moves, the remaining rooks (at A1, A4, D1, and D4) each have four moves.

%Y Cf. A275815, A278212, A278215.

%K nonn,more

%O 1,2

%A _Peter Kagey_, Nov 15 2016

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)