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.

Showing 1-5 of 5 results.

A320448 a(n) is the maximum number of distinct distances between n non-attacking rooks on an n X n chessboard.

Original entry on oeis.org

0, 1, 2, 4, 8, 11, 15, 20, 25, 31, 37, 44, 51, 59, 68
Offset: 1

Views

Author

Peter Kagey, Oct 12 2018

Keywords

Comments

A319476(n) <= a(n) <= n(n-1)/2.

Examples

			For n = 5 a placement of five rooks on a 5 X 5 board with a(5) = 8 distinct distances is:
  +---+---+---+---+---+
5 |   | * |   |   |   |
  +---+---+---+---+---+
4 | * |   |   |   |   |
  +---+---+---+---+---+
3 |   |   |   |   | * |
  +---+---+---+---+---+.
2 |   |   | * |   |   |
  +---+---+---+---+---+
1 |   |   |   | * |   |
  +---+---+---+---+---+
    A   B   C   D   E
The distances between pairs of pieces are:
1)   sqrt(2)  (A4 to B5 and C2 to D1)
2) 2*sqrt(2)  (A4 to C2)
3) 3*sqrt(2)  (A4 to D1)
4)   sqrt(17) (A4 to E3)
5)   sqrt(10) (B5 to C2)
6) 2*sqrt(5)  (B5 to D1)
7)   sqrt(13) (B5 to E3)
8)   sqrt(5)  (C2 to E3 and D1 to E3)

Links

Crossrefs

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

Extensions

a(11)-a(14) from Giovanni Resta, Oct 17 2018
a(15) from Bert Dobbelaere, Jan 01 2019

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

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

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
Showing 1-5 of 5 results.

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