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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
0, 4, 12, 28, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= A275815(n).

LINKS

Table of n, a(n) for n=1..5.

Peter Kagey, Examples for 1 <= n <= 5.

FORMULA

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

EXAMPLE

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

   +---+---+---+---+

  4| R |   |   | R |

   +---+---+---+---+

  3|   |   | R |   |

   +---+---+---+---+

  2|   | R |   |   |

   +---+---+---+---+

  1| R |   |   | R |

   +---+---+---+---+

     A   B   C   D

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

CROSSREFS

Cf. A275815, A278212, A278215.

Sequence in context: A220514 A301005 A178571 * A192736 A109629 A112087

Adjacent sequences:  A278208 A278209 A278210 * A278212 A278213 A278214

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Nov 15 2016

STATUS

approved

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Last modified April 25 08:35 EDT 2018. Contains 303055 sequences. (Running on oeis4.)