A167227 Number of 2-self-hedrites with n vertices.

1, 1, 2, 2, 3, 3, 3, 3, 5, 4, 4, 6, 5, 5, 8, 5, 6, 8, 6, 8, 10, 7, 7, 10, 10, 8, 12, 10, 9, 14, 9, 9, 14, 10, 14, 16, 11, 11, 16

Offset: 2

Author

Jonathan Vos Post, Oct 30 2009

Keywords

• nonn
• more

Comments

A 2-self-hedrite is a self-dual plane multigraph such that each its face has 4 sides except for 2 faces with 2 sides. - Andrey Zabolotskiy, Dec 16 2021

Links

• Mathieu Dutour Sikiric and Michel Deza, 4-regular and self-dual analogs of fullerenes, arXiv:0910.5323 [math.GT], 2009.

Crossrefs

Cf. A167156, A167157, A167158, A167159, A111361, A167228, A167229.

Formula

It appears that a(n+1) = A167156(2*n) - A167156(n) [discovered using Sequence Machine]. An equivalent assertion is that if a plane multigraph and its dual both have only 4-gonal faces except for 2 2-gonal ones, then they are isomorphic. - Andrey Zabolotskiy, Dec 16 2021