A007894 -id:A007894 - cp's OEIS frontend

A122661 Erroneous version of A007894.

6, 15, 17, 40, 49, 89, 116, 199, 271, 437, 580, 924, 1205, 1812, 2385, 3465, 4478, 6332, 8149, 11190, 14246

Offset: 17

dead

A111361 The number of 4-regular plane graphs with n vertices with all faces 3-gons or 4-gons.

0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 5, 2, 8, 5, 12, 8, 25, 13, 30, 23, 51, 33, 76, 51, 109, 78, 144, 106, 218, 150, 274, 212, 382, 279, 499, 366, 650, 493, 815, 623, 1083, 800, 1305, 1020, 1653, 1261, 2045, 1554, 2505, 1946, 3008, 2322, 3713, 2829, 4354, 3418, 5233, 4063, 6234

Offset: 2

Gunnar Brinkmann, Nov 07 2005

nonn

These are the 4-regular graphs corresponding to the 3-regular fullerenes. Only the two smallest possible face sizes are allowed. The numbers up to a(33) have been checked by 2 independent programs. Further numbers have not been checked independently.

			From _Allan Bickle_, May 13 2024: (Start)
The smallest example (n=6) is the octahedron (only 3-gons).
For n=8, the unique graph is the square of an 8-cycle.
For n=9, the unique graph is the dual of the Herschel graph. (End)

Andrey Zabolotskiy, Table of n, a(n) for n = 2..131 (from Hasheminezhad & McKay)
G. Brinkmann, O. Heidemeier and T. Harmuth, The construction of cubic and quartic planar maps with prescribed face degrees, Discrete Applied Mathematics 128: 541-554, (2003).
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
Michel-Marie Deza, Mathieu Dutour Sikiric and Mikhail Ivanovitch Shtogrin, Geometric Structure of Chemistry-Relevant Graphs, Springer, 2015; see Sec. 4.4.
Mathieu Dutour Sikiric and Michel Deza, 4-regular and self-dual analogs of fullerenes, arXiv:0910.5323 [math.GT], 2009.
Mahdieh Hasheminezhad and Brendan D. McKay, Recursive generation of simple planar quadrangulations with vertices of degree 3 and 4, Discussiones Mathematicae Graph Theory, 30 (2010), 123-136.
T. Tarnai, F. Kovács, P. W. Fowler and S. D. Guest, Wrapping the cube and other polyhedra, Proc. Roy. Soc. A 468(2145) (2012), 2652-2666. DOI: 10.1098/rspa.2012.0116.

Cf. A007894.
Cf. A167156, A167157, A167158, A167159.
Cf. A007022, A072552, A078666, A292515 (4-regular planar graphs with restrictions).

Leading zeros prepended, terms a(34) and beyond added from the book by Deza et al. (except for a(60) from the paper by Brinkmann et al.) by Andrey Zabolotskiy, Oct 09 2021

A046880 Number of isolated-pentagon (IPR) fullerenes with 2n vertices (or carbon atoms).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 1, 1, 2, 5, 7, 9, 24, 19, 35, 46, 86, 134, 187, 259, 450, 616, 823, 1233, 1799, 2355, 3342, 4468, 6063, 8148, 10774, 13977, 18769, 23589, 30683, 39393, 49878, 62372, 79362, 98541, 121354, 151201, 186611, 225245, 277930, 335569

Offset: 30

Gunnar Brinkmann and A. Dress (dress(AT)mathematik.uni-bielefeld.de)

Enantiomorphic pairs are regarded as the same here. Cf. A086423.

P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Cambridge Univ. Press, 1995, see p. 33.

Jan Goedgebeur, Table of n, a(n) for n = 30..200, terms a(30)..a(120) from Gunnar Brinkmann.
Gunnar Brinkmann and Andreas W. M. Dress, A constructive enumeration of fullerenes, J. Algorithms 23 (1997), no. 2, 345-358.
Gunnar Brinkmann, Jan Goedgebeur, Brendan D. McKay, The Generation of Fullerenes, arXiv:1207.7010v1 [math.CO], 2012.
Gunnar Brinkmann, Andreas Dress, fullgen.
Gunnar Brinkmann, Jan Goedgebeur, Brendan D. McKay, buckygen.
CombOS - Combinatorial Object Server, generate fullerenes
House of Graphs, Fullerenes.
A. M. Livshits and Yu. E. Lozovik, Cut-and-unfold approach to fullerene enumeration, J. Chem. Inf. Comput. Sci., (2004), vol. 44, 1517-1520.

Cf. A086423, A007894, A057210.

Added a(121)-a(200). a(30)-a(190) is independently confirmed by buckygen and fullgen, while a(191)-a(200) was only computed by buckygen. - Jan Goedgebeur, Aug 08 2012

A057210 Number of fullerenes with 2n vertices (or carbon atoms), counting enantiomorphic pairs as distinct.

Original entry on oeis.org

1, 0, 1, 1, 3, 3, 10, 9, 23, 30, 66, 80, 162, 209, 374, 507, 835, 1113, 1778, 2344, 3532, 4670, 6796, 8825, 12501, 16091, 22142, 28232, 38016, 47868, 63416, 79023, 102684, 126973, 162793, 199128, 252082, 306061, 382627, 461020

Offset: 10

N. J. A. Sloane, Aug 28 2003

nonn

P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Cambridge Univ. Press, 1995, see p. 32.

Gunnar Brinkmann, Table of n, a(n) for n = 10..100 (Received Aug 18, 2006)
Philip Engel and Peter Smillie The number of non-negative curvature triangulations of S^2, arXiv:1702.02614 [math.GT], 2017.
Philip Engel, Jan Goedgebeur, and Peter Smillie, Exact enumeration of fullerenes, arXiv:2304.01655 [math.GT], 2023.

Cf. A007894, A013957.

a(n) = (809/1306069401600)*sigma_9(n) + O(n^8) where sigma_9(n) is the ninth divisor power sum, A013957. - Philip Engel, Nov 29 2017

A111358 Numbers of planar triangulations with minimum degree 5 and without separating 3- or 4-cycles - that is 3- or 4-cycles where the interior and exterior contain at least one vertex.

Original entry on oeis.org

1, 0, 1, 1, 3, 4, 12, 23, 71, 187, 627, 1970, 6833, 23384, 82625, 292164, 1045329, 3750277, 13532724, 48977625, 177919099, 648145255, 2368046117, 8674199554, 31854078139, 117252592450, 432576302286, 1599320144703, 5925181102878

Offset: 12

Gunnar Brinkmann, Nov 07 2005

nonn

A006791 and this sequence are the same sequence. The correspondence is just that these objects are planar duals of each other. But the offset and step are different: if the cubic graph has 2*n vertices, the dual triangulation has n+2 vertices. - Brendan McKay, May 24 2017

Also the number of 5-connected triangulations on n vertices. - Manfred Scheucher, Mar 17 2023

			The icosahedron is the smallest triangulation with minimum degree 5 and it doesn't contain any separating 3- or 4-cycles. Examples can easily be seen as 2D and 3D pictures using the program CaGe cited above.

G. Brinkmann, CaGe.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph. [Cached copy, pdf file only, no active links, with permission]
G. Brinkmann and Brendan D. McKay, Construction of planar triangulations with minimum degree 5 , Disc. Math. vol 301, iss. 2-3 (2005) 147-163.
D. A. Holton and B. D. McKay, The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices, J. Combinat. Theory B vol 45, iss. 3 (1988) 305-319.
D. A. Holton and B. D. McKay, Erratum, J. Combinat. Theory B vol 47, iss. 2 (1989) 248.

Cf. A081621, A007894, A006791, A000109, A007021, A361578.

A086423 Number of isolated-pentagon fullerenes with 2n vertices (or carbon atoms).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 1, 1, 3, 6, 9, 12, 34, 33, 56, 78, 161, 252, 349, 483, 862, 1179, 1606, 2401, 3502, 4645, 6568, 8820, 11997, 16132, 21326, 27763, 37313, 46907, 61069, 78476, 99343, 124282, 158258, 196532, 242126, 301752, 372498, 449742

Offset: 30

N. J. A. Sloane, Sep 08 2003

nonn

Enantiomorphic pairs are counted as different here. Cf. A046880.

P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Cambridge Univ. Press, 1995, see p. 33.

Gunnar Brinkmann, Table of n, a(n) for n = 30..120

Cf. A046880, A007894, A057210.

More terms from Gunnar Brinkmann, Aug 24 2006

A111357 Numbers of planar triangulations with minimum degree 5 and without separating 3-cycles - that is 3-cycles where the interior and exterior contain at least one vertex.

Original entry on oeis.org

1, 0, 1, 1, 3, 4, 12, 23, 73, 191, 649, 2054, 7209, 24963, 89376, 320133, 1160752, 4218225, 15414908, 56474453, 207586410, 764855802, 2825168619, 10458049611, 38795658003, 144203518881, 537031911877, 2003618333624, 7488436558647

Offset: 12

Gunnar Brinkmann, Nov 07 2005

nonn

			The icosahedron is the smallest triangulation with minimum degree 5 and it doesn't contain any separating triangles. Examples can easily be seen as 2D and 3D pictures using the program CaGe cited above.

G. Brinkmann, CaGe.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
G. Brinkmann and Brendan D. McKay, Construction of planar triangulations with minimum degree 5 , Disc. Math. vol 301, iss. 2-3 (2005) 147-163.

Cf. A081621, A007894.

cp's OEIS Frontend

A122661 Erroneous version of A007894.

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A111361 The number of 4-regular plane graphs with n vertices with all faces 3-gons or 4-gons.

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A046880 Number of isolated-pentagon (IPR) fullerenes with 2n vertices (or carbon atoms).

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A057210 Number of fullerenes with 2n vertices (or carbon atoms), counting enantiomorphic pairs as distinct.

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A111358 Numbers of planar triangulations with minimum degree 5 and without separating 3- or 4-cycles - that is 3- or 4-cycles where the interior and exterior contain at least one vertex.

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A086423 Number of isolated-pentagon fullerenes with 2n vertices (or carbon atoms).

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Author

Keywords

Comments

References

Links

Crossrefs

Extensions

A111357 Numbers of planar triangulations with minimum degree 5 and without separating 3-cycles - that is 3-cycles where the interior and exterior contain at least one vertex.

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Author

Keywords

Examples

Links

Crossrefs