proposed

approved

editing

proposed

Cf. A000105, A098891, A367436, A367437, A367438, A367440, A367441, A367443.

Half the row sums of A367439.

Cf. A000105, A098891, A367436, A367437, A367438, A367439, A367440, A367441.

allocated Let PG(n) be the graph with one node for Pontus von Brömsseneach free n-celled polyomino and edges between nodes corresponding to polyominoes that can be obtained from each other by moving one cell, where the intermediate (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, 45, 254, 1258, 6181, 28062, 125714, 550402, 2394654, 10326665

1,4

Equivalently, there is an edge between two nodes if the corresponding n-celled polyominoes can be obtained from the same (n-1)-celled polyomino by adding one cell.

In the n-omino graph defined in A098891, the intermediate is not required to be a polyomino, so PG(n) is a spanning subgraph of that graph. For n = 5, for example, there is an edge between the V and W pentominoes in the graph in A098891, but not in PG(5).

<a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.

a(n) <= A098891(n).

Cf. A000105, A098891, A367436, A367437, A367438, A367439, A367440, A367441.

allocated

nonn,more

Pontus von Brömssen, Nov 18 2023

approved

editing

allocating

allocated

allocated for Pontus von Brömssen

allocating

approved