A320574 a(n) gives the number of configurations of non-attacking rooks up to symmetry on an n X n chessboard such that the number of distinct distances between the rooks is given by A320448(n).

1, 1, 2, 1, 1, 3, 6, 4, 4, 2, 6, 3, 18, 9

Offset: 1

Author

Peter Kagey, Oct 15 2018

Keywords

• nonn
• more

Comments

Conjecture: a(n) = A320573(n)/8 for all n > 3.

Examples

			For n = 6 the a(6) = 3 configurations with A320448(6) = 11 distinct distances are:
+---+---+---+---+---+---+
| * |   |   |   |   |   |
+---+---+---+---+---+---+
|   |   | * |   |   |   |
+---+---+---+---+---+---+
|   | * |   |   |   |   |
+---+---+---+---+---+---+,
|   |   |   |   | * |   |
+---+---+---+---+---+---+
|   |   |   |   |   | * |
+---+---+---+---+---+---+
|   |   |   | * |   |   |
+---+---+---+---+---+---+
+---+---+---+---+---+---+
| * |   |   |   |   |   |
+---+---+---+---+---+---+
|   |   | * |   |   |   |
+---+---+---+---+---+---+
|   |   |   |   |   | * |
+---+---+---+---+---+---+, and
|   |   |   | * |   |   |
+---+---+---+---+---+---+
|   |   |   |   | * |   |
+---+---+---+---+---+---+
|   | * |   |   |   |   |
+---+---+---+---+---+---+
+---+---+---+---+---+---+
| * |   |   |   |   |   |
+---+---+---+---+---+---+
|   | * |   |   |   |   |
+---+---+---+---+---+---+
|   |   |   |   | * |   |
+---+---+---+---+---+---+.
|   |   |   | * |   |   |
+---+---+---+---+---+---+
|   |   |   |   |   | * |
+---+---+---+---+---+---+
|   |   | * |   |   |   |
+---+---+---+---+---+---+
		

Links

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

Crossrefs

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

Extensions

a(10)-a(14) from Giovanni Resta, Oct 21 2018