A365862 Number of 4-fold rotationally symmetric pentomino tilings of the 5n X 5n square such that no two tiles can be replaced with two pentomominoes in a new configuration.

1, 0, 0, 0, 2, 0, 20, 54, 6464

Offset

0,5

Comments

a(n) is even for all n > 0 since no pentomino tiling can have both rotation and reflection symmetry.

Links

Table of n, a(n) for n=0..8.

Jamie Tucker-Foltz, Locked Polyomino Tilings, arXiv:2307.15996 [math.CO], 2023.

Jamie Tucker-Foltz, GitHub repository with Python code and pictures of all tilings.

Wikipedia, Pentomino.

Example

a(4) = 2:
._______________________________________.
|_. | ._. | ._|_. |_________|_________| |
| | |_| |_| |_. | ._|_. | ._. | ._| .___|
| |___| |___| | |_| ._| |_| |_| | |_|_. |
| | |_____| ._| | ._| |___| |___| .___| |
| |___. |___| |_|_| |_. |_____| |_| |___|
|_| ._|_| |_______| ._|___| | |_. |___. |
| | |___. |_. | |___|_______| ._|___| |_|
| |___| |_| | |_______| | ._| |_______| |
| | .___| ._| |_. | .___| | |_|_. |_. ._|
| |_| |___| |_| | |_|_. | |_. ._|_. |_| |
|_| |_. |___. | |___| | |_| |_| ._|_| | |
| .___|___| |_| | .___|___| | ._| .___| |
|_| ._____| |___|_|_____. | |_| |_|_. | |
| |_|_. |_. | ._____| ._|_|___| .___| |_|
|___. |_. |_|_|_. |_. |___. ._|_| |___| |
| ._|_| |_|_. ._|_. |_| | |_| ._|___. | |
| |___. | ._| |_. |_| ._| | ._|_. ._|_| |
|___| |_| | |_| | |___| | |_| ._| |_. | |
| .___|___|_____|___|_. |___| | |_| | |_|
|_|_________|_________|___|___|_____|___| (*2)

Crossrefs

Sequence in context: A264881 A280622 A211880 * A209868 A182661 A189772

Adjacent sequences: A365859 A365860 A365861 * A365863 A365864 A365865

Keyword

nonn,more

Author

Jamie Tucker-Foltz, Sep 29 2023

Extensions

a(8) from Jamie Tucker-Foltz, Oct 30 2023

Status

approved