A367436 Number of Hamiltonian cycles in the polyomino graph PG(n) defined in A367435.

1, 1, 0, 2, 4080

Offset: 1

Author

Pontus von Brömssen, Nov 18 2023

Keywords

• nonn
• more

Comments

A cycle and its reverse are not both counted.

We follow the convention in A003216 that the complete graphs on 1 and 2 nodes have 1 and 0 Hamiltonian cycles, respectively, so that a(1) = a(2) = 1 and a(3) = 0, but it could also be argued that a(1) = a(2) = 0 and/or a(3) = 1.

Links

• Pontus von Brömssen, A Hamiltonian cycle in the heptomino graph.
• Pontus von Brömssen, A Hamiltonian cycle in the hexomino graph.
• MathOverflow, Generating all pentominoes by cutting and pasting.
• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A003216, A367123, A367435.

Formula

a(n) <= A367123(n).

a(n) > 0 for 4 <= n <= 13.