A319476 a(n) is the minimum number of distinct distances between n non-attacking rooks on an n X n chessboard.

0, 1, 2, 2, 3, 5, 5, 6, 5, 7, 9, 7, 8, 11, 13, 9, 11, 14, 16, 17, 19, 21, 21, 14, 14

Offset: 1

Author

Peter Kagey, Oct 12 2018

Keywords

• nonn
• more

Comments

a(n) <= n - 1, which is the number of distinct distances the rooks are placed along a diagonal.

Conjecture: a(n^2) = A047800(n-1) - 1. - Peter Kagey, Nov 02 2018

Examples

			For n = 7 a board with a(7) = 5 distinct distances is
  +---+---+---+---+---+---+---+
7 |   |   | * |   |   |   |   |
  +---+---+---+---+---+---+---+
6 |   |   |   |   |   | * |   |
  +---+---+---+---+---+---+---+
5 | * |   |   |   |   |   |   |
  +---+---+---+---+---+---+---+
4 |   |   |   | * |   |   |   |
  +---+---+---+---+---+---+---+.
3 |   |   |   |   |   |   | * |
  +---+---+---+---+---+---+---+
2 |   | * |   |   |   |   |   |
  +---+---+---+---+---+---+---+
1 |   |   |   |   | * |   |   |
  +---+---+---+---+---+---+---+
    A   B   C   D   E   F   G
The distances between pairs of points are:
1)   sqrt(10) (e.g., A5 to B2),
2) 2*sqrt(2)  (e.g., A5 to C7),
3) 4*sqrt(2)  (e.g., B2 to F6),
4) 2*sqrt(10) (e.g., A5 to G3), and
5)   sqrt(26) (e.g., A5 to F6).
		

Links

• Giovanni Resta, Illustration of a(3)-a(14)

Crossrefs

Cf. A008404, A319476, A320575, A320576, A320448, A320573, A320574.

Extensions

a(11)-a(14) from Giovanni Resta, Oct 17 2018

a(15)-a(25) from Bert Dobbelaere, Dec 30 2018