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

Author

Lotfi Bouallagui, May 07 2018

Keywords

• nonn
• hard
• more

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