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

1,3

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

Crossrefs

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

Sequence in context: A070766 A111772 A233005 * A323930 A187982 A000228

Adjacent sequences: A018187 A018188 A018189 * A018191 A018192 A018193

Keyword

nonn,nice

Author

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

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

Status

approved