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

1, 1, 2, 2, 3, 2, 2, 1, 1, 6, 602, 324, 148, 48, 16, 3, 1, 186, 30, 6, 1

Offset

1,3

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

Table of n, a(n) for n=1..21.

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.).

Sequence in context: A219237 A138774 A156988 * A251140 A259977 A341434

Adjacent sequences: A304196 A304197 A304198 * A304200 A304201 A304202

Keyword

nonn,more

Author

Lotfi Bouallagui, May 07 2018

Status

approved