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 1-6 of 6 results.

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

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

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

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 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.