A018190 Number of planar simply-connected polyhexes (or benzenoid hydrocarbons) with n hexagons.

1, 1, 3, 7, 22, 81, 331, 1435, 6505, 30086, 141229, 669584, 3198256, 15367577, 74207910, 359863778, 1751594643, 8553649747, 41892642772, 205714411986, 1012565172403, 4994807695197, 24687124900540, 122238208783203

Offset: 1

Author

N. J. A. Sloane, Viviane Rochon (viviane(AT)crt.umontreal.ca), Gilles Caporossi (gillesc(AT)crt.umontreal.ca)

Keywords

• nonn
• nice

References

• 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.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..35 [from Vöge et al.]
• Gunnar Brinkmann, Gilles Caporossi and Pierre Hansen, A constructive enumeration of fusenes and benzenoids, Journal of Algorithms 45 (2002), pp. 155-166.
• Gunnar Brinkmann, Gilles Caporossi and Pierre Hansen, A Survey and New Results on Computer Enumeration of Polyhex and Fusene Hydrocarbons, J. Chem. Inf. Comput. Sci., vol. 43 (2003) 842-851.
• G. Caporossi, P. Hansen, Enumeration of Polyhex Hydrocarbons to h = 21, J. Chem. inf. Comput. Sci. 38 (4) (1998) 610-619, Table 1.
• James Chapman, Judith Foos, Andrew Nelson, Elizabeth J. Hartung, and Aaron Williams, Pairwise disagreements of Kekulé, Clar, and Fries numbers for benzenoids: a mathematical and computational investigation, arXiv:1804.06071 [math.PR], 2018.
• Frédéric Chyzak, Ivan Gutman, and Peter Paule, Predicting the number of hexagonal systems with 24 and 25 hexagons, Communications in Mathematical and Computer Chemistry (1999) No. 40, 139-151. See p. 141.
• J. L. Faulon, D. Visco, Jr., and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.
• J. V. Knop, W. R. Müller, K. Szymanski, and N. Trinajstić, Use of small computers for large computations: enumeration of polyhex hydrocarbons, J. Chem. Inf. Comput. Sci., 30 (1990), 159-160.
• J. V. Knop, K. Szymanski, Ž. Jeričević, and N. Trinajstić, On the total number of polyhexes, Match, No. 16 (1984), 119-134.
• Elena V. Konstantinova and Maxim V. Vidyuk, Discriminating tests of information and topological indices. Animals and trees, J. Chem. Inf. Comput. Sci. 43 (2003), 1860-1871.
• Lucia Moura and Ivan Stojmenovic, Backtracking and Isomorph-Free Generation of Polyhexes, Table 2.1 on p. 50 of Handbook of Applied Algorithms (2008). Note a(8) is given as 1453!
• S. Nikolić, N. Trinajstić, J. V. Knop, W. R. Müller, On the concept of the weighted spanning tree of dualist, J. Math. Chem. 4 (1990), 357-375.
• R. Tošić, D. Mašulović, I. Stojmenović, J. Brunvoll, B. N. Cyvin, and S. J. Cyvin, Enumeration of polyhex hydrocarbons to h = 17, J. Chem. Inf. Comput. Sci., 1995, 35, 181-187.
• N. Trinajstić, Z. Jerievi, J. V. Knop, W. R. Müller, and K. Szymanski, Computer Generation of Isomeric Structures, Pure & Appl. Chem., Vol. 55, No. 2, pp. 379-390, 1983.
• Markus Vöge, Anthony J. Guttmann, and Iwan Jensen, On the Number of Benzenoid Hydrocarbons, Journal of Chemical Information and Computer Sciences, 42(3) (2002), 456-466.
• Eric Weisstein's World of Mathematics, Polyhex.
• Eric Weisstein's World of Mathematics, Benzenoid
• Eric Weisstein's World of Mathematics, Fusene [That page refers to this sequence as "[simply-connected] catafusenes", but in fact the polyhexes counted by this sequence are not necessarily catacondensed (i.e. tree-like). - _Andrey Zabolotskiy_, Apr 11 2025]

Crossrefs

Cf. A000228, A002216, A018190, A038142-A038147.

Extensions

More terms from Joseph Myers, Nov 06 2003

Further terms added by N. J. A. Sloane from Brinkmann et al. (2003). Jun 04 2005