cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A343432 Sorted numbers of spanning trees in the graphs of the Archimedean solids.

Original entry on oeis.org

6000, 331776, 32400000, 101154816, 301056000000, 89904012853248, 208971104256000, 12418325780889600, 4982259375000000000, 375291866372898816000, 201550864919150779950956544000, 438201295386966498858139607040000000, 21789262703685125511464767107171876864000
Offset: 1

Views

Author

Pontus von Brömssen, Apr 15 2021

Keywords

Comments

The duals (Catalan solids) have the same number of spanning trees as their Archimedean counterparts.

Examples

			The solids are in order:
  truncated tetrahedron (6000),
  cuboctahedron (331776),
  truncated cube (32400000),
  truncated octahedron (101154816),
  rhombicuboctahedron (301056000000),
  snub cube (89904012853248),
  icosidodecahedron (208971104256000),
  truncated cuboctahedron (12418325780889600),
  truncated dodecahedron (4982259375000000000),
  truncated icosahedron (375291866372898816000),
  rhombicosidodecahedron (201550864919150779950956544000),
  snub dodecahedron (438201295386966498858139607040000000),
  truncated icosidodecahedron (21789262703685125511464767107171876864000).

Crossrefs

Cf. A343209, A343213, A343433.

A343434 Sorted numbers of (undirected) Hamiltonian cycles in the graphs of the Catalan solids (the Archimedean duals).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 6, 726, 1704, 348912, 1919220, 1685220540, 310880892720
Offset: 1

Views

Author

Pontus von Brömssen, Apr 19 2021

Keywords

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.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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