A321534 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 directions between the rooks is given by A321531(n).

1, 1, 1, 1, 2, 21, 11, 74, 89, 18

Offset

1,5

Comments

Conjecture: a(n) = A321532(n)/8 for n >= 4.

Links

Table of n, a(n) for n=1..10.

Example

For n = 5, the a(5) = 2 essentially different configurations of nonattacking rooks with the maximal number of directions between them are given by the following two chessboards:
   +---+---+---+---+---+
  5| X |   |   |   |   |
   +---+---+---+---+---+
  4|   |   | X |   |   |
   +---+---+---+---+---+
  3|   |   |   | X |   |
   +---+---+---+---+---+
  2|   |   |   |   | X |
   +---+---+---+---+---+
  1|   | X |   |   |   |
   +---+---+---+---+---+
     A   B   C   D   E
   +---+---+---+---+---+
  5| X |   |   |   |   |
   +---+---+---+---+---+
  4|   |   |   | X |   |
   +---+---+---+---+---+
  3|   |   | X |   |   |
   +---+---+---+---+---+
  2|   |   |   |   | X |
   +---+---+---+---+---+
  1|   | X |   |   |   |
   +---+---+---+---+---+
     A   B   C   D   E

Crossrefs

Cf. A321531, A321532.

Sequence in context: A298822 A072397 A077208 * A212483 A084313 A140268

Adjacent sequences: A321531 A321532 A321533 * A321535 A321536 A321537

Keyword

nonn,more

Author

Peter Kagey, Nov 12 2018

Status

approved