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.

User: Márk Péter Légrádi

Márk Péter Légrádi's wiki page.

Márk Péter Légrádi has authored 16 sequences. Here are the ten most recent ones:

A363382 Three-dimensional polyknights, identifying rotations and reflections.

Original entry on oeis.org

1, 1, 12, 203, 5552, 182490, 6455845, 237152245
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 30 2023

Keywords

Comments

Polyknights in two dimension (A030446) have 8 neighborhood vectors, [+-1, +-2] and [+-2, +-1]. In three dimensions the 24 neighborhood vectors are [0, +-1, +-2] (four choices of signs) and its six permutations.

A363383 Three-dimensional polyknights, identifying rotations but not reflections.

Original entry on oeis.org

1, 1, 16, 346, 10611, 360098, 12864217
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 30 2023

Keywords

Comments

The 24 neighborhood vectors are [0, +-1, +-2] (four choices of signs) and its six permutations.
Identifying reflections as well gives A363382.

Crossrefs

Cf. A363383 (fixed 3D polyknights).

A363384 Fixed three-dimensional polyknights.

Original entry on oeis.org

1, 12, 276, 7850, 251726, 8628406, 308645452
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 30 2023

Keywords

Comments

The 24 neighborhood vectors are [0, +-1, +-2] (four choices of signs) and its six permutations.

Crossrefs

Cf. A363382 (identifying rotations and reflections), A363383 (identifying only rotations).
Cf. A030445 (fixed polyknights in two dimensions).

A363210 Number of linear connected animals formed from n 4-gon or 6-gon connected truncated octahedra.

Original entry on oeis.org

1, 2, 5, 19, 95, 598, 4190, 30809, 230104, 1728305, 12993821
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 22 2023

Keywords

Comments

Rotations and reflections are identified.
Linear lattice animals have two end points with one neighbor, the remaining elements all have two neighbors.
The analog for polycubes is A363202. The analog for truncated octahedra is A363209. The analog for rhombic dodecahedra is A363208.

A363209 Number of linear connected animals formed from n rhombic dodecahedra.

Original entry on oeis.org

1, 1, 3, 10, 52, 288, 1826, 11702, 76586, 501429, 3289245, 21554198
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 22 2023

Keywords

Comments

Rotations and reflections are identified.
Linear lattice animals have two end points with one neighbor, the remaining elements all have two neighbors.
The analog for polycubes is A363202. The analog for truncated octahedra is A363208.

Crossrefs

Cf. A363210.

A363208 Number of linear connected animals formed from n 6-gon connected truncated octahedra.

Original entry on oeis.org

1, 1, 3, 7, 29, 114, 578, 2890, 15431, 82091, 442702, 2377819, 12820705
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 22 2023

Keywords

Comments

Rotations and reflections are identified.
Linear lattice animals have two end points with one neighbor, the remaining elements all have two neighbors.
The analog for polycubes is A363202. The analog for rhombic dodecahedra is A363209.

Crossrefs

Cf. A363210.

A363207 Number of polycubes avoiding corner connections.

Original entry on oeis.org

1, 1, 2, 6, 15, 47, 170, 654, 2699, 11539, 50919, 229529, 1054374, 4915265
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 22 2023

Keywords

Comments

Rotations and reflections are identified.
Avoiding corner connections is avoiding neighbors at [+-1, +-1,+-1]. Allowing corner connections gives A038119.

Crossrefs

Cf. A363200 (truncated octahedra avoiding neighbors at [0,0,+-2], [0,+-2,0], and [+-2,0,0]).

A363200 Number of connected animals formed from n 6-gon connected truncated octahedra, avoiding connected squares.

Original entry on oeis.org

1, 1, 2, 5, 15, 55, 248, 1256, 6844, 38930, 226961, 1345641, 8072770, 48882245, 298237393
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 22 2023

Keywords

Comments

Rotations and reflections are identified.
Avoiding connected squares is the same as avoiding neighbors at [0,0,+-2], [0,+-2,0], and [+-2,0,0].
Allowing connected squares gives A038171.

Examples

			The animals for n <= 5 are:
n=1:
  0,0,0
n=2:
  0,0,0; 1,1,1
n=3:
  0,0,0; 0,2,2; 1,1,1
  0,0,0; 1,1,1; 2,2,2
n=4:
  0,0,0; 0,2,2; 1,1,1; 1,3,3
  0,0,0; 0,2,2; 1,1,1; 2,0,2
  0,0,0; 1,1,1; 1,3,3; 2,2,2
  0,0,0; 1,1,1; 2,2,2; 3,3,3
  0,0,1; 1,1,0; 1,3,2; 2,2,1
n=5:
  0,0,0; 0,2,2; 0,4,4; 1,1,1; 1,3,3
  0,0,0; 0,2,2; 1,1,1; 1,3,3; 2,0,2
  0,0,0; 0,2,2; 1,1,1; 1,3,3; 2,2,4
  0,0,0; 0,2,2; 1,1,1; 1,3,3; 2,4,4
  0,0,0; 0,2,2; 1,1,1; 2,0,2; 2,2,0
  0,0,0; 0,2,4; 1,1,1; 1,3,3; 2,2,2
  0,0,0; 0,4,4; 1,1,1; 1,3,3; 2,2,2
  0,0,0; 1,1,1; 1,3,3; 2,2,2; 3,1,3
  0,0,0; 1,1,1; 2,2,2; 2,4,4; 3,3,3
  0,0,0; 1,1,1; 2,2,2; 3,3,3; 4,4,4
  0,0,1; 0,2,3; 1,1,0; 1,3,2; 2,2,1
  0,0,1; 0,2,3; 1,1,2; 1,3,0; 2,2,1
  0,0,1; 0,4,1; 1,1,0; 1,3,2; 2,2,1
  0,0,1; 1,1,0; 2,2,1; 2,4,3; 3,3,2
  0,0,1; 1,1,0; 2,2,1; 3,3,2; 4,4,1

Extensions

a(14) and a(15) from Joerg Arndt, Dec 09 2023

A363202 Number of free linear polycubes of size n, identifying rotations and reflections.

Original entry on oeis.org

1, 1, 2, 4, 12, 34, 125, 450, 1780, 7021, 28521, 115553, 472578, 1927634, 7890893, 32221475, 131812746, 538059836, 2198986587, 8970624060, 36628143111, 149328243327, 609238673619
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 21 2023

Keywords

Comments

Linear polycubes have two end points with one neighbor, the remaining cubes all have two neighbors.
Identifying rotations but not reflections gives A363201.
The fixed version is A118339.

Links

Crossrefs

Cf. A304196 (tree-like polycubes), A363208, A363209, A363210.

Extensions

a(17)-a(22) from Arthur O'Dwyer added by Andrey Zabolotskiy, Jun 07 2023
a(23) added by Arthur O'Dwyer, Aug 11 2023

A363201 Number of free linear polycubes of size n, identifying rotations but not reflections.

Original entry on oeis.org

1, 1, 2, 5, 16, 54, 212, 827, 3369, 13653, 56052, 229004, 939935, 3843859, 15753903, 64380796, 263475472, 1075780425, 4397161320, 17939394036, 73251877235, 298646347226, 1218453344740
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 21 2023

Keywords

Comments

Linear polycubes have two end points with one neighbor, the remaining cubes all have two neighbors.
Additionally identifying reflections gives A363202.
The fixed version is A118339.

Links

Crossrefs

Cf. A363199 (tree-like polycubes).

Extensions

a(15)-a(23) from Arthur O'Dwyer added by Andrey Zabolotskiy, Jun 07 2023

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

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