A167227 -id:A167227 - cp's OEIS frontend

A215622 Number of loopless ({1,2,3},6)-spheres with n vertices.

0, 1, 1, 3, 2, 7, 5, 12, 10, 19, 16, 29, 24, 42, 35, 59, 48, 79, 69, 100, 86, 133, 112, 165, 144, 205, 176, 251, 214, 299, 265, 360, 305, 429, 375, 488, 436, 581, 495, 677, 582, 758, 679, 869, 749, 1000, 868, 1101, 989, 1259, 1076, 1410, 1228

Offset: 1

Jonathan Vos Post, Aug 17 2012

nonn

Equivalently, ({2,3},6)-spheres, or 6-regular planar graphs with digonal and trigonal faces only. - Andrey Zabolotskiy, Mar 22 2019

Andrey Zabolotskiy, Table of n, a(n) for n = 1..100
Michel Deza and Mathieu Dutour Sikiric, Zigzag and Central Circuit Structure of ({1,2,3},6)-spheres, Taiwanese Journal of Mathematics, 16 (June 2012), No. 3, 913-940; see Table 1, p. 916.
Michel-Marie Deza, Mathieu Dutour Sikiric and Mikhail Ivanovitch Shtogrin, Geometric Structure of Chemistry-Relevant Graphs, Springer, 2015; see p. 107.

Cf. A088534, A111361, A167227, A210146.

A167228 Number of 3-self-hedrites with n vertices.

Original entry on oeis.org

0, 1, 1, 4, 6, 7, 11, 16, 16, 26, 29, 30, 42, 47, 48, 64, 72, 70, 89, 104, 90, 119, 131, 124, 162, 170, 158, 190, 210, 202, 239, 256, 232, 290, 308, 286, 342, 359, 332

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, A167229.

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.

A210146 Number of square fullerenes with 2n vertices.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 3, 1, 3, 3, 3, 2, 8, 3, 7, 7, 7, 5, 14, 6, 12, 12, 13, 10, 23, 12, 19, 21, 22, 16, 36, 21, 29, 31, 34, 24, 53, 32, 42, 47, 50, 35, 75, 46, 59, 65, 70, 48, 99, 65, 79, 89, 97, 68, 133, 90, 99, 115, 127, 86, 171, 118, 133, 152, 165, 110, 220

Offset: 4

N. J. A. Sloane, Mar 18 2012

nonn

3-regular plane graphs with 4-gonal and 6-gonal faces only. - Andrey Zabolotskiy, Dec 23 2021

Andrey Zabolotskiy, Table of n, a(n) for n = 4..130
Antoine Deza, Michel Deza and Viatcheslav Grishukhin, Fullerenes and coordination polyhedra versus half-cube embeddings. Discrete metric spaces (Villeurbanne, 1996). Discrete Math. 192 (1998), no. 1-3, 41--80. MR1656726 (99k:92049)
Michel-Marie Deza, Mathieu Dutour Sikiric and Mikhail Ivanovitch Shtogrin, Geometric Structure of Chemistry-Relevant Graphs, Springer, 2015; see Table 3.2.

Cf. A088534, A111361, A167227, A215622.

Terms a(23) and beyond from the book by Deza et al. added by Andrey Zabolotskiy, Dec 23 2021

cp's OEIS Frontend

A215622 Number of loopless ({1,2,3},6)-spheres with n vertices.

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A167228 Number of 3-self-hedrites with n vertices.

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

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A210146 Number of square fullerenes with 2n vertices.

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