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

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

Offset: 1

Author

Lotfi Bouallagui, May 07 2018

Keywords

• nonn
• 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. 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.).