

A007894


Number of fullerenes with 2n vertices (or carbon atoms).


10



1, 0, 1, 1, 2, 3, 6, 6, 15, 17, 40, 45, 89, 116, 199, 271, 437, 580, 924, 1205, 1812, 2385, 3465, 4478, 6332, 8149, 11190, 14246, 19151, 24109, 31924, 39718, 51592, 63761, 81738, 99918, 126409, 153493, 191839, 231017, 285914, 341658, 419013
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OFFSET

10,5


COMMENTS

Enantiomorphic pairs are regarded as the same here. Cf. A057210.
Contradictory results from the program "buckygen" from Brinkmann et al. (2012) and the program "fullgen" from Brinkmann and Dress (1997) led to the detection of a nonalgorithmic error in fullgen. This bug has now been fixed and the results are in complete agreement. a(10)a(190) were independently confirmed by buckygen and fullgen, while a(191)a(200) were computed only by buckygen.  Jan Goedgebeur, Aug 08 2012


REFERENCES

A. T. Balaban, X. Liu, D. J. Klein, D. Babic, T. G. Schmalz, W. A. Seitz and M. Randic, "Graph invariants for fullerenes", J. Chem. Inf. Comput. Sci., vol. 35 (1995) 396404.
Brinkmann, Gunnar and Dress, Andreas W. M.; A constructive enumeration of fullerenes. J. Algorithms 23 (1997), no. 2, 345358.
M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads and knots in fullerenes, J. Chem. Inf. Comput. Sci., 44 (2004), 12821293.
J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, WileyVCH, 2005.
P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Cambridge Univ. Press, 1995, see p. 32.
P. W. Fowler, D. E. Manolopoulos and R. P. Ryan, "Isomerization of fullerenes", Carbon, 30 1235 1992.
A. M. Livshits and Yu. E. Lozovik, Cutandunfold approach to Fullerene enumeration, J. Chem. Inf. Comput. Sci., 44 (2004), 15171520.
A. Milicevic and N. Trinajstic, "Combinatorial Enumeration in Chemistry", Chem. Modell., Vol. 4, (2006), pp. 405469.
M. Petkovsek and T. Pisanski, Counting disconnected structures: chemical trees, fullerenes, Igraphs and others, Croatica Chem. Acta, 78 (2005), 563567.


LINKS

Jan Goedgebeur, Table of n, a(n) for n = 10..200.
Gunnar Brinkmann, Jan Goedgebeur, Brendan D. McKay, The Generation of Fullerenes, arXiv:1207.7010v1 [math.CO]
Gunnar Brinkmann, Andreas Dress, fullgen.
Gunnar Brinkmann, Jan Goedgebeur, Brendan D. McKay, buckygen.
Jan Goedgebeur, Brendan D. McKay, Fullerenes with distant pentagons, arXiv:1508.02878 [math.CO], (12August2015)
House of Graphs, Fullerenes.
Eric Weisstein's World of Mathematics, Fullerene
Wikipedia, Fullerene


CROSSREFS

Cf. A057210, A046880.
Sequence in context: A129648 A129649 A129650 * A102625 A117777 A223547
Adjacent sequences: A007891 A007892 A007893 * A007895 A007896 A007897


KEYWORD

nonn,easy,nice


AUTHOR

Boris Shraiman (boris(AT)physics.att.com), G. Brinkmann (Gunnar.Brinkmann(AT)ugent.be) and A. Dress (dress(AT)mathematik.unibielefeld.de)


EXTENSIONS

Corrected a(68)a(100) and added a(101)a(200).  Jan Goedgebeur, Aug 08 2012


STATUS

approved



