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A321531 a(n) is the maximum number of distinct directions between n non-attacking rooks on an n X n chessboard. 2
0, 1, 2, 4, 6, 8, 11, 14, 18, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Directions are determined up to scaling and dihedral action of the square, as in (m,k)-riders. For example, the moves (1,2) and (2,-4) are considered to have the same direction.

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

For n = 5, a 5 X 5 board with a(5) = 6 distinct directions is

   +---+---+---+---+---+

  5| X |   |   |   |   |

   +---+---+---+---+---+

  4|   |   | X |   |   |

   +---+---+---+---+---+

  3|   |   |   | X |   |

   +---+---+---+---+---+

  2|   |   |   |   | X |

   +---+---+---+---+---+

  1|   | x |   |   |   |

   +---+---+---+---+---+

     A   B   C   D   E

Where the six distinct directions are:

1) 1:4 by (A5,B1).

2) 1:2 by (A5,C4).

3) 2:3 by (A5,D3).

4) 3:4 by (A5,E2).

5) 1:3 by (B1,C4) and (B1,E2).

6) 1:1 by (B1,D3), (C4,D3), (C4,E2), and (D3,E2).

CROSSREFS

Cf. A320448 (analogous with distance instead of direction).

Sequence in context: A183144 A194162 A084627 * A194224 A194252 A205727

Adjacent sequences:  A321528 A321529 A321530 * A321532 A321533 A321534

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Nov 12 2018

STATUS

approved

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Last modified October 5 06:51 EDT 2022. Contains 357252 sequences. (Running on oeis4.)