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.

A234622 Numbers of undirected cycles in the n X n king graph.

Original entry on oeis.org

7, 348, 136597, 545217435, 21964731190911, 9389890985897322572, 41930442683035614068268389, 1912714607714074785106312737308553, 888957501697133413663023517792044869026260, 4209348789084188565760570660849691414465827388642586
Offset: 2

Views

Author

Eric W. Weisstein, Dec 28 2013

Keywords

Crossrefs

Extensions

a(7)-a(11) from Andrew Howroyd, Apr 06 2016

A368499 Number of non-congruent simple polygons with 2n sides on the unbounded chessboard such that each side is an edge of the corresponding knight graph.

Original entry on oeis.org

3, 13, 178, 3034, 64877, 1503790, 36930111
Offset: 2

Views

Author

Kaloyan Kapralov, Dec 27 2023

Keywords

Comments

A knight graph is a graph that represents all legal moves of the knight chess piece on a chessboard. Each vertex of this graph represents a square of the chessboard, and each edge connects two squares that are a knight's move apart from each other.
Two polygons in the knight graph are called congruent if one can be transformed into the other by applying one or more of the operations of translation, rotation, and reflection on the chessboard; otherwise, they are non-congruent.
This sequence, in contrast to A366778, considers only simple, i.e., non-self-intersecting polygons.

Examples

			For n=2 the a(2)=3 solutions (in standard chess notation) are:
  (a1,c2,d4,b3), (a2,c1,d2,c3), (a2,c1,d3,b3).
For n=3 the a(3)=13 solutions are:
  (a1,b3,a5,c4,e3,c2), (a1,b3,a5,c6,b4,c2), (a1,b3,a5,c6,d4,c2),
  (a1,b3,c5,e6,d4,c2), (a2,b4,c2,d4,e2,c1), (a2,b4,c6,d4,b3,c1),
  (a2,b4,c6,d4,e2,c1), (a2,b4,c6,e5,d3,c1), (a2,b4,d5,c3,e2,c1),
  (a2,b4,d5,f4,d3,c1), (a2,b4,d5,f4,e2,c1), (a2,c1,d3,f4,d5,c3),
  (a2,c1,e2,g3,e4,c3).
		

Crossrefs

A289204 Number of (undirected) paths in the n X n knight graph.

Original entry on oeis.org

0, 0, 56, 14980, 19005336, 278982789260
Offset: 1

Views

Author

Eric W. Weisstein, Jun 28 2017

Keywords

Crossrefs

Extensions

a(5)-a(6) from Andrew Howroyd, Jul 01 2017

A297666 Number of chordless cycles in the n X n knight graph.

Original entry on oeis.org

0, 0, 1, 64, 651, 4680, 56919, 2578420, 205224704
Offset: 1

Views

Author

Eric W. Weisstein, Jan 02 2018

Keywords

Crossrefs

Extensions

a(6)-a(9) from Andrew Howroyd, Jan 08 2018

A366778 Number of nonequivalent cycles of length 2n in the (2n+1) X (2n+1) knight graph.

Original entry on oeis.org

3, 25, 480, 12000, 350256, 10780549, 344680960
Offset: 2

Views

Author

Stoyan Kapralov, Dec 15 2023

Keywords

Comments

A knight graph is a graph that represents all legal moves of the knight chess piece on a chessboard. Each vertex of this graph represents a square of the chessboard, and each edge connects two squares that are a knight's move apart from each other.
Two cycles in the knight graph are called equivalent if one can be obtained from another by applying one or more of the operations of translation, rotation, and symmetry on the chessboard; otherwise, they are nonequivalent.

Examples

			For n=2 the a(2)=3 solutions (in standard chess notation) are: (a1, c2, d4, b3), (a2, c1, d2, c3), and (a2, c1, d3, b3).
Note that each of these three cycles is non-self-intersecting. For the remaining values of n there are two kind of cycles - self-intersecting and non-self-intersecting. For example, a self-intersecting cycle of length 6 is (a1, c2, b4, a2, c1, b3), while the cycle (a1, c2, e1, f3, d4, b3) is non-self-intersecting.
		

Crossrefs

Showing 1-5 of 5 results.