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: Lotfi Bouallagui

Lotfi Bouallagui's wiki page.

Lotfi Bouallagui has authored 5 sequences.

A304195 Number of fully-leafed free tree-like polyominoes of size n.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 12, 3, 1, 6, 74, 11, 2, 21, 408, 40, 4, 76, 2053, 148, 11, 279
Offset: 1

Views

Author

Lotfi Bouallagui, May 07 2018

Keywords

Comments

A free tree-like polyomino of size n is a connected set of n cells in the square lattice, up to translation, rotation and reflection, whose dual graph has no cycles. It is called fully-leafed when it has the maximal number of leaves over all the same sized free tree-like polyominoes.

Examples

			a(5) = 1:
.  #
. ###
.  #
a(6) = 2:
.  #   .  #
. #### . ####
.  #   .   #
a(7) = 12:
. # # . # #  .  # #  .    #  .  #    .   #
. ### . #### . ##### . ##### . ##### . #####
. # # . #    .       .  #    .  #    .  #
.
.  # # .  # # .  #   .  #   .  #   .   #
. #### . #### .  #   . ##   . ##   . #####
.  #   .   #  . #### .  ### .  ### .   #
.      .      .  #   .  #   .   #  .

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. A131482 (free tree-like polyominoes), A304197, A304199 (fully-leafed free tree-like polycubes in 3 and 4 dimensions resp.).

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.).

A304199 Number of fully-leafed free tree-like 4d-polycubes of size n.

Original entry on oeis.org

1, 1, 2, 2, 3, 2, 2, 1, 1, 6, 602, 324, 148, 48, 16, 3, 1, 186, 30, 6, 1
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. It is said to be fully-leafed when it has the maximal number of leaves over all the same sized free tree-like 4d-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. A304198 (free tree-like 4d-polycubes), A304195, A304197 (fully-leafed free tree-like polyominoes and 3d-polycubes resp.).

A304196 Number of free tree-like polycubes of size n in three dimensions.

Original entry on oeis.org

1, 1, 2, 6, 21, 91, 484, 2817, 17788, 116741, 788081, 5414701, 37703459, 265182187
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.

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. A118356 (fixed tree-like 3d-polycubes), A304198 (free tree-like 4d-polycubes), A131482 (free tree-like polyominoes).

Extensions

Terms a(13) and a(14) from Joerg Arndt and Márk Péter Légrádi, May 21 2023

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).

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