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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 (list; graph; refs; listen; history; text; internal format)



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


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.

Brinkmann, Gunnar and Dress, Andreas W. M.; A constructive enumeration of fullerenes. J. Algorithms 23 (1997), no. 2, 345-358.

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.


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

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

Gunnar Brinkmann, Andreas Dress, fullgen.

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

CombOS - Combinatorial Object Server, generate fullerenes

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

Jan Goedgebeur, 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


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


Cf. A057210, A046880.

Sequence in context: A129650 A319055 A339546 * A102625 A117777 A223547

Adjacent sequences:  A007891 A007892 A007893 * A007895 A007896 A007897




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


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



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Last modified January 28 03:43 EST 2021. Contains 340490 sequences. (Running on oeis4.)