A304198 -id:A304198 - cp's OEIS frontend

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

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

Offset: 1

Lotfi Bouallagui, May 07 2018

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.

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.

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

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

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

Lotfi Bouallagui, May 07 2018

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.

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.

Cf. A304198 (free tree-like 4d-polycubes), A304195, A304197 (fully-leafed free tree-like polyominoes and 3d-polycubes resp.).

cp's OEIS Frontend

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

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