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A343434

Sorted numbers of (undirected) Hamiltonian cycles in the graphs of the Catalan solids (the Archimedean duals).

0, 0, 0, 0, 0, 0, 6, 726, 1704, 348912, 1919220, 1685220540, 310880892720

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OFFSET

1,7

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

Six of the Catalan solids are not Hamiltonian, so a(n) = 0 for n <= 6. These solids are: the rhombic dodecahedron, the triakis octahedron, the deltoidal icositetrahedron, the rhombic triacontahedron, the triakis icosahedron, and the deltoidal hexecontahedron.

The remaining (Hamiltonian) solids are in order:

triakis tetrahedron (6),

pentagonal icositetrahedron (726),

tetrakis hexahedron (1704),

disdyakis dodecahedron (348912),

pentagonal hexecontahedron (1919220),

pentakis dodecahedron (1685220540),

disdyakis triacontahedron (310880892720).

CROSSREFS

Cf. A268283, A343211, A343433.

Sequence in context: A168467 A080369 A036981 * A202080 A271528 A316748

Adjacent sequences: A343431 A343432 A343433 * A343435 A343436 A343437

KEYWORD

nonn,fini,full

AUTHOR

Pontus von Brömssen, Apr 19 2021

STATUS

approved