cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A321532 a(n) gives the number of configurations of non-attacking rooks on an n X n chessboard such that the number of distinct directions between the rooks is given by A321531(n).

Original entry on oeis.org

1, 2, 4, 8, 16, 168, 88, 592, 712
Offset: 1

Views

Author

Peter Kagey, Nov 12 2018

Keywords

Examples

			For n = 5, the a(5) = 16 configurations of nonattacking rooks with the maximal number of directions between them are given by the following two chessboards under all eight symmetries of the square.
   +---+---+---+---+---+
  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.

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).

Original entry on oeis.org

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

Views

Author

Peter Kagey, Nov 12 2018

Keywords

Comments

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

Examples

			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.
Showing 1-2 of 2 results.

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