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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, 76 (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..6.

Michael S. Branicky, Examples for n = 6.

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.

PROG

(Python) # see link in A275815

CROSSREFS

Cf. A275815, A278212, A278215.

Sequence in context: A220514 A301005 A178571 * A342235 A192736 A109629

Adjacent sequences:  A278208 A278209 A278210 * A278212 A278213 A278214

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Nov 15 2016

EXTENSIONS

a(6) from Michael S. Branicky, Feb 12 2021

STATUS

approved

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Last modified May 22 09:12 EDT 2022. Contains 353941 sequences. (Running on oeis4.)