A389997 Ordered numbers of partitions of the faces of the Archimedean solids into connected subsets.

1595, 845792, 2225225, 3624912

Offset

1,1

Comments

Ordered composition numbers of the 1-skeletons of the Catalan solids.

Ordered numbers of bridgeless spanning subgraphs of the 1-skeletons of the Archimedean solids.

The first two terms of the corresponding sequence for the Catalan solids are 31371 (triakistetrahedron) and 135521 (rhombic dodecahedron). The third term is greater than 10^8.

Links

Table of n, a(n) for n=1..4.

Example

The first solids are in order:
  truncated tetrahedron (1595),
  cuboctahedron (845792),
  truncated cube (2225225),
  truncated octahedron (3624912).

Crossrefs

Cf. A389996 (platonic solids), A389998 (Johnson solids).

Cf. A092536 (edges), A092537 (faces), A092538 (vertices), A343432 (spanning trees), A343433 (Hamiltonian cycles), A389999 (partitions of the faces into 2 connected parts).

Sequence in context: A316336 A028893 A029561 * A015281 A132654 A224946

Adjacent sequences: A389994 A389995 A389996 * A389998 A389999 A390000

Keyword

nonn,fini,more

Author

Pontus von Brömssen, Oct 31 2025

Status

approved