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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
0, 4, 17, 40, 76 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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

FORMULA

Conjecture: a(n) = 8(n-2)^2 for n >= 6. - Alec Jones, Nov 16 2016

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

EXAMPLE

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

   +---+---+---+

  3| Q |   | Q |

   +---+---+---+

  2| Q |   |   |

   +---+---+---+

  1|   | Q |   |

   +---+---+---+

     A   B   C

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.

CROSSREFS

Cf. A278211, A278212, A278214.

Sequence in context: A022266 A273309 A145995 * A018973 A212575 A162148

Adjacent sequences:  A275812 A275813 A275814 * A275816 A275817 A275818

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Nov 14 2016

STATUS

approved

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Last modified January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)