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

Offset: 1

Author

Pontus von Brömssen, Apr 19 2021

Keywords

• nonn
• fini
• full

Examples

			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.