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A379747
The number of Hamiltonian cycles with rotational symmetry of order 3 on the triangular grid, n vertices on each side.
1
0, 1, 1, 0, 2, 6, 0, 52, 270, 0, 17130, 189154, 0, 51417622
OFFSET
1,5
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.
EXAMPLE
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.
CROSSREFS
Cf. A112676.
Sequence in context: A106458 A354351 A213323 * A293016 A122685 A109581
KEYWORD
nonn,more,new
AUTHOR
Nicolay Avilov, Jan 01 2025
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
STATUS
approved