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.

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

A304197 Number of fully-leafed free tree-like 3d-polycubes of size n.

Original entry on oeis.org

1, 1, 2, 2, 2, 1, 1, 4, 100, 42, 16, 3, 1, 31, 1, 989, 164, 17, 2, 384, 10
Offset: 1

Views

Author

Lotfi Bouallagui, May 07 2018

Keywords

Comments

A free tree-like polycube of size n in three dimensions is a face-connected set of n cells in the cubic lattice, up to translation, rotation and reflection, whose dual graph has no cycles. It is said to be fully-leafed when it has the maximal number of leaves over all the same sized free tree-like 3d-polycubes.

Links

  • Alexandre Blondin Massé, Julien de Carufel, Alain Goupil, and Maxime Samson, Fully-leafed tree-like polyominoes and polycubes, In Combinatorial algorithms, volume 10765 of Lecture Notes of Computer Science, 28th International workshop, IWOCA 2017, Newcastle, NSW, Australia, Springer, 2018.

Crossrefs

Cf. A304196 (free tree-like 3d-polycubes), A304195, A304199 (fully-leafed free tree-like polyominoes and 4d-polycubes resp.).

A304198 Number of free tree-like 4d-polycubes of size n.

Original entry on oeis.org

1, 1, 2, 6, 24, 122, 838, 6759, 61600, 600875, 6139448
Offset: 1

Views

Author

Lotfi Bouallagui, May 07 2018

Keywords

Comments

A free tree-like polycube of size n in four dimensions is a hyperface-connected set of n cells in the 4d-hypercubic lattice, up to translation, rotation and reflection, whose dual graph has no cycles.

Links

  • Alexandre Blondin Massé, Julien de Carufel, Alain Goupil, and Maxime Samson, Fully-leafed tree-like polyominoes and polycubes, In Combinatorial algorithms, volume 10765 of Lecture Notes of Computer Science, 28th International workshop, IWOCA 2017, Newcastle, NSW, Australia, Springer, 2018.

Crossrefs

Cf. A191094 (fixed tree-like 4d-polycubes), A131482 (free tree-like polyominoes), A304196 (free tree-like 3d-polycubes).

A363199 Number of free tree-like polycubes of size n, identifying rotations but not reflections.

Original entry on oeis.org

1, 1, 2, 7, 27, 138, 822, 5154, 33880, 227495, 1554266, 10749089, 75106906
Offset: 1

Views

Author

Joerg Arndt and Márk Péter Légrádi, May 21 2023

Keywords

Comments

Tree-like means that the graph connecting midpoints of adjacent cubes is a tree.
Additionally identifying reflections gives A304196.
The fixed version is A118356.

Extensions

a(12) and a(13) from Joerg Arndt, Dec 11 2023

A368031 Number of free treelike midpoint-free polycubes of size n, identifying rotations and reflections.

Original entry on oeis.org

1, 1, 1, 3, 4, 12, 23, 47, 91, 202, 428, 911, 1862, 3638, 6637, 11780, 20764, 36904, 64855, 111552, 186147, 302526, 479076, 739080, 1106514, 1610045, 2278632, 3146000, 4254002, 5682571, 7558064, 10081716, 13532752, 18293656, 24830210, 33733178, 45720871
Offset: 1

Views

Author

Joerg Arndt, Dec 08 2023

Keywords

Comments

Treelike means that the graph connecting midpoints of adjacent cubes has no cycles.
Midpoint-free means that no three cubes are in positions (x,y,z), (x+dx,y+dx,z+dz), and (x+2*dx,y+2*dx,z+2*dz).

Examples

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

Crossrefs

Cf. A304196, A368029.
Showing 1-5 of 5 results.

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