login
A319476
a(n) is the minimum number of distinct distances between n non-attacking rooks on an n X n chessboard.
7
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
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).
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