A304199 -id:A304199 - cp's OEIS frontend

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

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

Offset: 1

Lotfi Bouallagui, May 07 2018

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.

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

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. 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

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. 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.

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. A304196 (free tree-like 3d-polycubes), A304195, A304199 (fully-leafed free tree-like polyominoes and 4d-polycubes resp.).

cp's OEIS Frontend

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

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