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%I #55 May 06 2021 21:21:34
%S 1,1,3,7,22,81,331,1435,6505,30086,141229,669584,3198256,15367577,
%T 74207910,359863778,1751594643,8553649747,41892642772,205714411986,
%U 1012565172403,4994807695197,24687124900540,122238208783203
%N Number of planar simply-connected polyhexes (or benzenoid hydrocarbons) with n hexagons.
%D J. Brunvoll, B. N. Cyvin, and S. J. Cyvin, Studies of some chemically relevant polygonal systems: mono-q-polyhexes, ACH Models in Chem., 133 (3) (1996), 277-298.
%H N. J. A. Sloane, <a href="/A018190/b018190.txt">Table of n, a(n) for n = 1..35</a> [from Vöge et al.]
%H Gunnar Brinkmann, Gilles Caporossi and Pierre Hansen, <a href="https://doi.org/10.1016/S0196-6774(02)00215-8">A constructive enumeration of fusenes and benzenoids</a>, Journal of Algorithms 45 (2002), pp. 155-166.
%H Gunnar Brinkmann, Gilles Caporossi and Pierre Hansen, <a href="https://doi.org/10.1021/ci025526c">A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons</a>, J. Chem. Inf. Comput. Sci., vol. 43 (2003) 842-851.
%H G. Caporossi, P. Hansen, <a href="http://dx.doi.org/10.1021/ci970116n">Enumeration of Polyhex Hydrocarbons to h = 21</a>, J. Chem. inf. Comput. Sci. 38 (4) (1998) 610-619, Table 1.
%H James Chapman, Judith Foos, Andrew Nelson, Elizabeth J. Hartung, and Aaron Williams, <a href="https://www.researchgate.net/profile/Aaron_Williams10/publication/324362787_Pairwise_Disagreements_of_Kekule_Clar_and_Fries_Numbers_for_Benzenoids_A_Mathematical_and_Computational_Investigation/links/5acbb357a6fdcc8bfc85fe5f/Pairwise-Disagreements-of-Kekule-Clar-and-Fries-Numbers-for-Benzenoids-A-Mathematical-and-Computational-Investigation.pdf">Pairwise disagreements of Kekulé, Clar, and Fries numbers for benzenoids: a mathematical and computational investigation</a>, arXiv:1804.06071 [math.PR], 2018.
%H Frédéric Chyzak, Ivan Gutman, and Peter Paule, <a href="https://match.pmf.kg.ac.rs/electronic_versions/Match40/match40_139-151.pdf">Predicting the number of hexagonal systems with 24 and 25 hexagons</a>, Communications in Mathematical and Computer Chemistry (1999) No. 40, 139-151. See p. 141.
%H J. L. Faulon, D. Visco, Jr., and D. Roe, <a href="https://doi.org/10.1002/0471720895.ch3">Enumerating Molecules</a>, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
%H J. V. Knop, W. R. Müller, K. Szymanski, and N. Trinajstić, <a href="https://doi.org/10.1021/ci00066a010">Use of small computers for large computations: enumeration of polyhex hydrocarbons</a>, J. Chem. Inf. Comput. Sci., 30 (1990), 159-160.
%H J. V. Knop, K. Szymanski, Ž. Jeričević, and N. Trinajstić, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match16/match16_119-134.pdf">On the total number of polyhexes</a>, Match, No. 16 (1984), 119-134.
%H Elena V. Konstantinova and Maxim V. Vidyuk, <a href="https://pubs.acs.org/action/doSearch?field1=Contrib&text1=Elena+V.++Konstantinova">Discriminating tests of information and topological indices. Animals and trees</a>, J. Chem. Inf. Comput. Sci. 43 (2003), 1860-1871.
%H Lucia Moura and Ivan Stojmenovic, <a href="https://doi.org/10.1002/9780470175668.ch2">Backtracking and Isomorph-Free Generation of Polyhexes</a>, Table 2.1 on p. 50 of Handbook of Applied Algorithms (2008). Note a(8) is given as 1453!
%H S. Nikolić, N. Trinajstić, J. V. Knop, W. R. Müller, <a href="https://www.researchgate.net/publication/225857878_On_the_concept_of_the_weighted_spanning_tree_of_dualist">On the concept of the weighted spanning tree of dualist</a>, J. Math. Chem. 4 (1990), 357-375.
%H R. Tošić, D. Mašulović, I. Stojmenović, J. Brunvoll, B. N. Cyvin, and S. J. Cyvin, <a href="https://doi.org/10.1021/ci00024a002">Enumeration of polyhex hydrocarbons to h = 17</a>, J. Chem. Inf. Comput. Sci., 1995, 35, 181-187.
%H N. Trinajstić, Z. Jerievi, J. V. Knop, W. R. Müller, and K. Szymanski, <a href="https://doi.org/10.1351/pac198855020379">Computer Generation of Isomeric Structures</a>, Pure & Appl. Chem., Vol. 55, No. 2, pp. 379-390, 1983.
%H Markus Vöge, Anthony J. Guttmann, and Iwan Jensen, <a href="https://doi.org/10.1021/ci010098g">On the Number of Benzenoid Hydrocarbons</a>, Journal of Chemical Information and Computer Sciences, 42(3) (2002), 456-466.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polyhex.html">Polyhex.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Benzenoid.html">Benzenoid</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fusene.html">Fusene</a>
%Y Cf. A000228, A002216, A018190, A038142-A038147.
%K nonn,nice
%O 1,3
%A _N. J. A. Sloane_, Viviane Rochon (viviane(AT)crt.umontreal.ca), Gilles Caporossi (gillesc(AT)crt.umontreal.ca)
%E More terms from _Joseph Myers_, Nov 06 2003
%E Further terms added by _N. J. A. Sloane_ from Brinkmann et al. (2003). Jun 04 2005
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