A167228 -id:A167228 - cp's OEIS frontend

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

Jonathan Vos Post, Oct 30 2009

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

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

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

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

A167229 Number of 4-self-hedrites with n vertices.

Original entry on oeis.org

0, 0, 1, 1, 2, 4, 6, 8, 15, 16, 24, 33, 40, 48, 69, 73, 92, 114, 130, 148, 191, 198, 234, 276, 304, 332, 407, 421, 476, 550, 584, 631, 748, 760, 857, 956, 1002, 1070, 1239

Offset: 2

Jonathan Vos Post, Oct 30 2009

nonn

Mathieu Dutour Sikiric, Michel Deza, 4-regular and self-dual analogs of fullerenes, Oct 28, 2009.

Cf. A167156, A167157, A167158, A167159, A111361, A167227, A167228.

cp's OEIS Frontend

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

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