A390203 Let PG(n) be the graph with one node for each free n-celled polyomino in the {4,5} tessellation of the hyperbolic plane, and edges between nodes corresponding to polyominoes that can be obtained from each other by moving one cell, where the intermediate polyform (the set of cells remaining when the cell to be moved is detached) is required to be a connected polyomino. a(n) is the number of edges in PG(n).

0, 0, 1, 8, 71, 519, 3405, 20826, 123989, 725342, 4223861

Offset

1,4

Comments

This version of the sequence requires the intermediate polyform to be connected. See link "Excluded example transformation" for an example transformation that is consequently excluded here but included in A390202.

This sequence was calculated in the context of a project in collaboration with Érika Roldán, and Rosemberg Toalá-Enríquez.

Links

Table of n, a(n) for n=1..11.

John Mason, Graph of {4,5} tetrominoes

John Mason, Excluded example transformation

Crossrefs

Cf. A119611, A367435, A390202.

Sequence in context: A291892 A217328 A193102 * A390202 A038145 A198856

Adjacent sequences: A390200 A390201 A390202 * A390204 A390205 A390206

Keyword

nonn,more

Author

John Mason, Nov 03 2025

Status

approved