

A321531


a(n) is the maximum number of distinct directions between n nonattacking rooks on an n X n chessboard.


2




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



