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A018190 Number of planar simply-connected polyhexes (or benzenoid hydrocarbons) with n hexagons. 27
1, 1, 3, 7, 22, 81, 331, 1435, 6505, 30086, 141229, 669584, 3198256, 15367577, 74207910, 359863778, 1751594643, 8553649747, 41892642772, 205714411986, 1012565172403, 4994807695197, 24687124900540, 122238208783203 (list; graph; refs; listen; history; text; internal format)



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., 43 (2003), 842-851.

J. Brunvoll et al., Studies of some chemically relevant polygonal systems: mono-q-polyhexes, ACH Models in Chem., 133 (3) (1996), 277-298.

J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.

J. V. Knop et al., On the total number of polyhexes, Match, No. 16 (1984), 119-134.

J. V. Knop et al., Use of small computers for large computations..., J. Chem. Inf. Comput. Sci., 30 (1990), 159-160.

E. V. Konstantinova and M. V. Vidyuk, Discriminating tests of information and topological indices; animals and trees; J. Chem. Inf. Comput. Sci., 43 (2003), 1860-1871.

S. Nikolic et al., On the concept of the weighted spanning tree of dualist, J. Math. Chem. 4 (1990), 357-375.

Tosic R., Masulovic D., Stojmenovic I., Brunvoll J., Cyvin B. N. and Cyvin S. J., Enumeration of polyhex hydrocarbons to h = 17, J. Chem. Inf. Comput. Sci., 1995, 35, 181-187.

N. Trinajstich, Z. Jerievi, J. V. Knop, W. R. Muller and K. Szymanski, COMPUTER GENERATION OF ISOMERIC STRUCTURES, Pure & Appl. Chem., Vol. 55, No. 2, pp. 379-39O, 1983.

Markus Voege, Anthony J. Guttmann and Iwan Jensen, On the Number of Benzenoid Hydrocarbons, Journal of Chemical Information and Computer Sciences, 42(3) (2002), 456-466.


N. J. A. Sloane, Table of n, a(n) for n = 1..35 [from Voege et al.]

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, Aaron Williams, Pairwise disagreements of Kekulé, Clar, and Fries numbers for benzenoids: a mathematical and computational investigation, arXiv:1804.06071 [math.PR], 2018.

Eric Weisstein's World of Mathematics, Polyhex.

Eric Weisstein's World of Mathematics, Benzenoid

Eric Weisstein's World of Mathematics, Fusene


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

Sequence in context: A070766 A111772 A233005 * A187982 A000228 A108070

Adjacent sequences:  A018187 A018188 A018189 * A018191 A018192 A018193




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


More terms from Joseph Myers, Nov 06 2003

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



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Last modified November 20 16:53 EST 2018. Contains 317412 sequences. (Running on oeis4.)