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A278212 Maximum total number of possible moves that any number of bishops of the same color can make on an n X n chessboard. 4
0, 2, 8, 20, 38 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= A275815(n).

Conjecture: a(n) = floor(A275815(n)/2). - Peter Kagey, Nov 24 2016

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 bishops on the 4n-4 border locations shows that a(n) >= 4(n-2)^2. On the other hand, a(n) <= 4n^2 since each location is in the path of at most 4 bishops. - Chai Wah Wu, Nov 20 2016

EXAMPLE

The following 5 X 5 chessboard illustrates a(5) = 38:

   +---+---+---+---+---+

  5| B | B | B |   | B |

   +---+---+---+---+---+

  4|   |   |   |   | B |

   +---+---+---+---+---+

  3| B | B |   |   | B |

   +---+---+---+---+---+

  2|   |   |   |   | B |

   +---+---+---+---+---+

  1| B | B | B |   | B |

   +---+---+---+---+---+

     A   B   C   D   E

The bishops at A1, A5, B1, B5, E1, E2, E4, and E5 each have three moves; the bishops at A3, C1, C5, and E3 each have two moves; and the bishop at B3 has six moves.

CROSSREFS

Cf. A278211, A275815, A278213.

Sequence in context: A327100 A130238 A038460 * A077588 A025219 A032767

Adjacent sequences:  A278209 A278210 A278211 * A278213 A278214 A278215

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Nov 15 2016

STATUS

approved

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Last modified October 18 15:17 EDT 2019. Contains 328161 sequences. (Running on oeis4.)