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%I #65 Dec 08 2023 12:05:23
%S 1,0,1,1,2,3,6,6,15,17,40,45,89,116,199,271,437,580,924,1205,1812,
%T 2385,3465,4478,6332,8149,11190,14246,19151,24109,31924,39718,51592,
%U 63761,81738,99918,126409,153493,191839,231017,285914,341658,419013
%N Number of fullerenes with 2n vertices (or carbon atoms).
%C Enantiomorphic pairs are regarded as the same here. Cf. A057210.
%C 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
%D 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.
%D M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads and knots in fullerenes, J. Chem. Inf. Comput. Sci., 44 (2004), 1282-1293.
%D J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
%D P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Cambridge Univ. Press, 1995, see p. 32.
%D P. W. Fowler, D. E. Manolopoulos and R. P. Ryan, "Isomerization of fullerenes", Carbon, 30 1235 1992.
%D A. M. Livshits and Yu. E. Lozovik, Cut-and-unfold approach to Fullerene enumeration, J. Chem. Inf. Comput. Sci., 44 (2004), 1517-1520.
%D Milicevic, A., and N. Trinajstic. "Combinatorial enumeration in chemistry." Chapter 8 in Chemical Modelling: Application and Theory, Vol. 4 (2006): 405-469.
%D M. Petkovsek and T. Pisanski, Counting disconnected structures: chemical trees, fullerenes, I-graphs and others, Croatica Chem. Acta, 78 (2005), 563-567.
%H Jan Goedgebeur, <a href="/A007894/b007894.txt">Table of n, a(n) for n = 10..200</a>.
%H Gunnar Brinkmann, Jan Goedgebeur, and Brendan D. McKay, <a href="http://arxiv.org/abs/1207.7010">The Generation of Fullerenes</a>, arXiv:1207.7010 [math.CO], 2012.
%H Gunnar Brinkmann and Andreas Dress, <a href="http://users.cecs.anu.edu.au/~bdm/plantri/">fullgen</a>.
%H Gunnar Brinkmann and Andreas W. M. Dress, <a href="https://doi.org/10.1006/jagm.1996.0806">A constructive enumeration of fullerenes</a>, Journal of Algorithms, Vol. 23, No. 2 (1997), 345-358.
%H Gunnar Brinkmann, Jan Goedgebeur, and Brendan D. McKay, <a href="http://caagt.ugent.be/buckygen/">buckygen</a>.
%H CombOS - Combinatorial Object Server, <a href="http://combos.org/fullgen">generate fullerenes</a>
%H Philip Engel and Peter Smillie, <a href="https://arxiv.org/abs/1702.02614">The number of non-negative curvature triangulations of S^2</a>, arXiv:1702.02614 [math.GT], 2017.
%H Paul Gailiunas, <a href="https://archive.bridgesmathart.org/2023/bridges2023-337.html">Kagome from Deltahedra</a>, Bridges Conf. Proc.; Math., Art, Music, Architecture, Culture (2023) 337-344.
%H Jan Goedgebeur and Brendan D. McKay, <a href="http://arxiv.org/abs/1508.02878">Fullerenes with distant pentagons</a>, arXiv:1508.02878 [math.CO], (12-August-2015).
%H House of Graphs, <a href="https://houseofgraphs.org/meta-directory/fullerenes">Fullerenes</a>.
%H Diaaeldin Taha, Wei Zhao, J. Maxwell Riestenberg, and Michael Strube, <a href="https://arxiv.org/abs/2312.01502">Normed Spaces for Graph Embedding</a>, arXiv:2312.01502 [cs.LG], 2023. See p. 22.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fullerene.html">Fullerene</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Fullerene">Fullerene</a>
%F 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
%Y Cf. A057210, A046880.
%K nonn,easy,nice
%O 10,5
%A Boris Shraiman (boris(AT)physics.att.com), _Gunnar Brinkmann_ and A. Dress (dress(AT)mathematik.uni-bielefeld.de)
%E Corrected a(68)-a(100) and added a(101)-a(200). - _Jan Goedgebeur_, Aug 08 2012
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