A007894 Number of fullerenes with 2n vertices (or carbon atoms).

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

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 non-algorithmic 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) 396-404.

M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads and knots in fullerenes, J. Chem. Inf. Comput. Sci., 44 (2004), 1282-1293.

J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 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, Cut-and-unfold approach to Fullerene enumeration, J. Chem. Inf. Comput. Sci., 44 (2004), 1517-1520.

Milicevic, A., and N. Trinajstic. "Combinatorial enumeration in chemistry." Chapter 8 in Chemical Modelling: Application and Theory, Vol. 4 (2006): 405-469.

M. Petkovsek and T. Pisanski, Counting disconnected structures: chemical trees, fullerenes, I-graphs and others, Croatica Chem. Acta, 78 (2005), 563-567.

Links

Jan Goedgebeur, Table of n, a(n) for n = 10..200.

Gunnar Brinkmann, Jan Goedgebeur, and Brendan D. McKay, The Generation of Fullerenes, arXiv:1207.7010 [math.CO], 2012.

Gunnar Brinkmann and Andreas Dress, fullgen.

Gunnar Brinkmann and Andreas W. M. Dress, A constructive enumeration of fullerenes, Journal of Algorithms, Vol. 23, No. 2 (1997), 345-358.

Gunnar Brinkmann, Jan Goedgebeur, and Brendan D. McKay, buckygen.

CombOS - Combinatorial Object Server, generate fullerenes

Philip Engel and Peter Smillie, The number of non-negative curvature triangulations of S^2, arXiv:1702.02614 [math.GT], 2017.

Jan Goedgebeur and Brendan D. McKay, Fullerenes with distant pentagons, arXiv:1508.02878 [math.CO], (12-August-2015).

House of Graphs, Fullerenes.

Eric Weisstein's World of Mathematics, Fullerene

Wikipedia, Fullerene

Formula

a(n) = (809/2612138803200)*sigma_9(n) + O(n^8) where sigma_9(n) is the ninth divisor power sum, cf. A013957. - Philip Engel, Nov 29 2017

Crossrefs

Cf. A057210, A046880.

Sequence in context: A355403 A319055 A339546 * A102625 A117777 A223547

Adjacent sequences: A007891 A007892 A007893 * A007895 A007896 A007897

Keyword

nonn,easy,nice

Author

Boris Shraiman (boris(AT)physics.att.com), Gunnar Brinkmann and A. Dress (dress(AT)mathematik.uni-bielefeld.de)

Extensions

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

Status

approved