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 1-3 of 3 results.

A110216 Total number of coverings of a cubic board with the minimal number of knights.

Original entry on oeis.org

1, 1, 12, 156, 888
Offset: 1

Views

Author

Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Jul 17 2005

Keywords

Examples

			a(3) = 12, since reflections or rotations of
OOO KKK OOO
OKO OKO OKO
OOO OOO OOO generate twelve different coverings.

Crossrefs

This sequence is a 3-dimensional analog of A103315. a(n) = A110219(n, n, n). A102215 gives the number of inequivalent solutions.

Formula

Sequence A110214 gives minimal number of knights needed to cover an n X n X n board. This sequence gives total number of solutions using A110214(n) knights.

A110217 Cone C(n,m,k) read by planes and rows, for 1 <= k <= m <= n: minimal number of knights needed to cover a k X m X n board.

Original entry on oeis.org

1, 2, 4, 8, 3, 4, 8, 4, 6, 6, 4, 4, 8, 4, 6, 6, 4, 6, 7, 8, 5, 4, 8, 4, 6, 6, 4, 6, 7, 8, 5, 6, 8, 10, 13, 6, 4, 6, 4, 7, 6, 4, 8, 8, 12, 6, 8, 10, 12
Offset: 1

Views

Author

Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Jul 17 2005

Keywords

Examples

			Cone starts:
1..2....3......4........5............6.................
...4.8..4.8....4.8......4.8..........4..6
........4.6.6..4.6.6....4.6.6........4..7..6
...............4.6.7.8..4.6.7..8.....4..8..8.12
........................5.6.8.10.13..6..8.10.12.?
.....................................8.11.12..?....

Crossrefs

C(n, n, 1) = A006075(n), C(n, k, 1) = A098604(n, k), C(n, n, n) = A110214(n). A110218 gives number of inequivalent ways to cover the board using C(n, m, k) knights, A110219 gives total number.

Formula

How many knights with move vector (2, 1, 0) are needed to occupy or attack every field of a k X m X n board? Knights may attack each other.

A110215 Inequivalent coverings of a cubic board with the minimal number of knights.

Original entry on oeis.org

1, 1, 1, 8, 37
Offset: 1

Views

Author

Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Jul 17 2005

Keywords

Comments

This sequence is a 3-dimensional analog of A006076.
Sequence A110214 gives minimal number of knights needed to cover an n X n X n board. This sequence gives the number of inequivalent solutions to cover an n X n X n board using A110214(n) knights.

Examples

			a(3) = 1, since up to rotations and reflections,
OOO KKK OOO
OKO OKO OKO
OOO OOO OOO is the only covering for n = 3.

Crossrefs

Cf. A006076, A110214, A110218.
A110216 gives total number of solutions.

Formula

a(n) = A110218(n, n, n).
Showing 1-3 of 3 results.

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

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