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
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.
A. Milicevic 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.
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.
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
M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads, and knots in fullerenes, J. Chem. Inf. Comput. Sci., 44 (2004), 1282-1293.
Philip Engel and Peter Smillie, The number of non-negative curvature triangulations of S^2, arXiv:1702.02614 [math.GT], 2017.
Thomas Fernique, Telstar Ball Gone Wild (pictures and properties of all a(30) = 1812 fullerenes with 60 vertices).
P. W. Fowler, D. E. Manolopoulos and R. P. Ryan, Isomerisations of the fullerenes, Carbon, 30, 1235-1250 (1992).
Paul Gailiunas, Kagome from Deltahedra, Bridges Conf. Proc.; Math., Art, Music, Architecture, Culture (2023) 337-344.
Jan Goedgebeur and Brendan D. McKay, Fullerenes with distant pentagons, arXiv:1508.02878 [math.CO], (12-August-2015).
House of Graphs, Fullerenes.
A. M. Livshits and Yu. E. Lozovik, Cut-and-unfold approach to fullerene enumeration, J. Chem. Inf. Comput. Sci., 44 (2004), 1517-1520.
Diaaeldin Taha, Wei Zhao, J. Maxwell Riestenberg, and Michael Strube, Normed Spaces for Graph Embedding, arXiv:2312.01502 [cs.LG], 2023. See p. 22.
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
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
