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

1,3

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

Links

Table of n, a(n) for n=1..25.

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

Example

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).

Crossrefs

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

Sequence in context: A123575 A014200 A293522 * A140200 A289199 A378358

Adjacent sequences: A319473 A319474 A319475 * A319477 A319478 A319479

Keyword

nonn,more

Author

Peter Kagey, Oct 12 2018

Extensions

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

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

Status

approved