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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.

Showing 1-7 of 7 results.

A320573 a(n) gives the number of configurations of non-attacking rooks on an n X n chessboard such that the number of distinct distances between the rooks is given by A320448(n).

Original entry on oeis.org

1, 2, 6, 8, 8, 24, 48, 32, 32, 16, 48, 24, 144, 72
Offset: 1

Views

Author

Peter Kagey, Oct 15 2018

Keywords

Examples

			For n = 6 the a(6) = 24 solutions are the eight symmetries of
+---+---+---+---+---+---+
| * |   |   |   |   |   |
+---+---+---+---+---+---+
|   |   | * |   |   |   |
+---+---+---+---+---+---+
|   | * |   |   |   |   |
+---+---+---+---+---+---+,
|   |   |   |   | * |   |
+---+---+---+---+---+---+
|   |   |   |   |   | * |
+---+---+---+---+---+---+
|   |   |   | * |   |   |
+---+---+---+---+---+---+
+---+---+---+---+---+---+
| * |   |   |   |   |   |
+---+---+---+---+---+---+
|   |   | * |   |   |   |
+---+---+---+---+---+---+
|   |   |   |   |   | * |
+---+---+---+---+---+---+, and
|   |   |   | * |   |   |
+---+---+---+---+---+---+
|   |   |   |   | * |   |
+---+---+---+---+---+---+
|   | * |   |   |   |   |
+---+---+---+---+---+---+
+---+---+---+---+---+---+
| * |   |   |   |   |   |
+---+---+---+---+---+---+
|   | * |   |   |   |   |
+---+---+---+---+---+---+
|   |   |   |   | * |   |
+---+---+---+---+---+---+.
|   |   |   | * |   |   |
+---+---+---+---+---+---+
|   |   |   |   |   | * |
+---+---+---+---+---+---+
|   |   | * |   |   |   |
+---+---+---+---+---+---+

Crossrefs

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

Extensions

a(11)-a(14) from Giovanni Resta, Oct 21 2018

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).

Original entry on oeis.org

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

Views

Author

Peter Kagey, Oct 15 2018

Keywords

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

Crossrefs

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

Extensions

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

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

Original entry on oeis.org

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

Views

Author

Peter Kagey, Oct 12 2018

Keywords

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

Examples

			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).

Links

Crossrefs

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

Extensions

a(11)-a(14) from Giovanni Resta, Oct 17 2018
a(15)-a(25) from Bert Dobbelaere, Dec 30 2018

A320575 a(n) gives the number of configurations of n non-attacking rooks on an n X n chessboard such that the number of distinct distances between the rooks is given by A319476(n).

Original entry on oeis.org

1, 2, 6, 2, 2, 28, 2, 4, 2, 8, 4, 2, 2, 4
Offset: 1

Views

Author

Peter Kagey, Oct 15 2018

Keywords

Examples

			For n = 7 the a(7) = 2 boards are mirror images of each other:
  +---+---+---+---+---+---+---+
7 |   |   | * |   |   |   |   |
  +---+---+---+---+---+---+---+
6 |   |   |   |   |   | * |   |
  +---+---+---+---+---+---+---+
5 | * |   |   |   |   |   |   |
  +---+---+---+---+---+---+---+
4 |   |   |   | * |   |   |   |
  +---+---+---+---+---+---+---+.
3 |   |   |   |   |   |   | * |
  +---+---+---+---+---+---+---+
2 |   | * |   |   |   |   |   |
  +---+---+---+---+---+---+---+
1 |   |   |   |   | * |   |   |
  +---+---+---+---+---+---+---+
    A   B   C   D   E   F   G
  +---+---+---+---+---+---+---+
7 |   |   |   |   | * |   |   |
  +---+---+---+---+---+---+---+
6 |   | * |   |   |   |   |   |
  +---+---+---+---+---+---+---+
5 |   |   |   |   |   |   | * |
  +---+---+---+---+---+---+---+
4 |   |   |   | * |   |   |   |
  +---+---+---+---+---+---+---+.
3 | * |   |   |   |   |   |   |
  +---+---+---+---+---+---+---+
2 |   |   |   |   |   | * |   |
  +---+---+---+---+---+---+---+
1 |   |   | * |   |   |   |   |
  +---+---+---+---+---+---+---+
    A   B   C   D   E   F   G

Crossrefs

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

Extensions

a(10) corrected and a(11)-a(14) from Giovanni Resta, Oct 21 2018

A320576 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 A319476(n).

Original entry on oeis.org

1, 1, 2, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Peter Kagey, Oct 15 2018

Keywords

Examples

			For n = 7 the a(7) = 1 board with A319476(7) = 5 distinct distances is
  +---+---+---+---+---+---+---+
7 |   |   | * |   |   |   |   |
  +---+---+---+---+---+---+---+
6 |   |   |   |   |   | * |   |
  +---+---+---+---+---+---+---+
5 | * |   |   |   |   |   |   |
  +---+---+---+---+---+---+---+
4 |   |   |   | * |   |   |   |
  +---+---+---+---+---+---+---+.
3 |   |   |   |   |   |   | * |
  +---+---+---+---+---+---+---+
2 |   | * |   |   |   |   |   |
  +---+---+---+---+---+---+---+
1 |   |   |   |   | * |   |   |
  +---+---+---+---+---+---+---+
    A   B   C   D   E   F   G

Links

Crossrefs

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

Extensions

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

A321531 a(n) is the maximum number of distinct directions between n non-attacking rooks on an n X n chessboard.

Original entry on oeis.org

0, 1, 2, 4, 6, 8, 11, 14, 18, 23
Offset: 1

Views

Author

Peter Kagey, Nov 12 2018

Keywords

Comments

Directions are determined up to scaling and dihedral action of the square, as in (m,k)-riders. For example, the moves (1,2) and (2,-4) are considered to have the same direction.

Examples

			For n = 5, a 5 X 5 board with a(5) = 6 distinct directions is
   +---+---+---+---+---+
  5| X |   |   |   |   |
   +---+---+---+---+---+
  4|   |   | X |   |   |
   +---+---+---+---+---+
  3|   |   |   | X |   |
   +---+---+---+---+---+
  2|   |   |   |   | X |
   +---+---+---+---+---+
  1|   | x |   |   |   |
   +---+---+---+---+---+
     A   B   C   D   E
Where the six distinct directions are:
1) 1:4 by (A5,B1).
2) 1:2 by (A5,C4).
3) 2:3 by (A5,D3).
4) 3:4 by (A5,E2).
5) 1:3 by (B1,C4) and (B1,E2).
6) 1:1 by (B1,D3), (C4,D3), (C4,E2), and (D3,E2).

Crossrefs

Cf. A320448 (analogous with distance instead of direction).

A306272 Sum of distinct distances between n non-attacking rooks over all n X n chessboards.

Original entry on oeis.org

0, 2, 12, 78, 686, 6056, 59002, 616522, 7009264, 86023126
Offset: 1

Views

Author

Peter Kagey, Feb 01 2019

Keywords

Comments

a(n)/n! gives the expected number of distinct distances of n non-attacking rooks on a random n X n chessboard.
n!*A319476(n) <= a(n) <= n!*A320448(n).

Crossrefs

Cf. A319476, A320448.
Showing 1-7 of 7 results.

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