A379747 The number of Hamiltonian cycles with rotational symmetry of order 3 on the triangular grid, n vertices on each side.

0, 1, 1, 0, 2, 6, 0, 52, 270, 0, 17130, 189154, 0, 51417622

Offset: 1

Author

Nicolay Avilov, Jan 01 2025

Keywords

• nonn
• more

Comments

If n = 3*k + 1, then the triangular grid has a central node, so for such n there are no Hamiltonian cycles and a(n) = 0.

Examples

			a(3) = 1, the only Hamiltonian cycle being the obvious one running around the edge of the triangle;
a(4) = 0 because there are no Hamiltonian cycles;
a(5) = 2 because there are exactly two Hamiltonian cycles.
		

Links

• Nicolay Avilov, Examples of cycles counted by a(1) - a(8).

Crossrefs

Cf. A112676.

Extensions

a(9)-a(10) from Andrey Zabolotskiy, Jan 02 2025

a(11)-a(13) from Talmon Silver, Jan 04 2025

a(14) from Talmon Silver, Jan 06 2025