A038142 Number of planar cata-polyhexes with n cells.

1, 1, 2, 5, 12, 36, 118, 411, 1489, 5572, 21115, 81121, 314075, 1224528, 4799205

Offset

1,3

Comments

Number of cata-condensed benzenoid hydrocarbons with n hexagons.

a(n) is the number of n-celled polyhexes with perimeter 4n+2. 4n+2 is the maximal perimeter of an n-celled polyhex. a(n) is the number of n-celled polyhexes that have a tree as their connectedness graph (vertices of this graph correspond to cells and two vertices are connected if the corresponding cells have a common edge). - Tanya Khovanova, Jul 27 2007

References

N. Trinajstić, S. Nikolić, J. V. Knop, W. R. Müller and K. Szymanski, Computational Chemical Graph Theory: Characterization, Enumeration, and Generation of Chemical Structures by Computer Methods, Ellis Horwood, 1991.

Links

Table of n, a(n) for n=1..15.

A. T. Balaban, J. Brunvoll, B. N. Cyvin and S. J. Cyvin, Enumeration of branched catacondensed benzenoid hydrocarbons and their numbers of Kekulé structures, Tetrahedron, 44(1), 221-228 (1998). See Table 1.

Andrew Clarke, Isoperimetrical Polyhexes

Wenchen He and Wenjie He, Generation and enumeration of planar polycyclic aromatic hydrocarbons, Tetrahedron 42.19 (1986): 5291-5299. See Table 3.

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

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. 379-390, 1983.

Eric Weisstein's World of Mathematics, Polyhex.

Eric Weisstein's World of Mathematics, Fusene.

Formula

a(n) = A003104(n) + A323851(n). - Andrey Zabolotskiy, Feb 15 2023

Crossrefs

Cf. A018190, A038143.

a(n) <= A000228(n), a(n) <= A057779(2n+1).

Sequence in context: A197444 A094717 A323933 * A287427 A267397 A267398

Adjacent sequences: A038139 A038140 A038141 * A038143 A038144 A038145

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Extensions

a(11) from Tanya Khovanova, Jul 27 2007

a(12)-a(14) from John Mason, May 13 2021

a(15) from Trinajstić et al. (Table 4.2) added by Andrey Zabolotskiy, Feb 08 2023

Status

approved