A003104 Number of hexagonal n-element polyominoes whose graph is a path. (Formerly M1208)

1, 1, 2, 4, 10, 24, 67, 182, 520, 1474, 4248, 12196, 35168, 101226, 291565, 838764, 2412033, 6929754, 19896915, 57084939

Offset

1,3

Comments

In other words, number of 2-sided strip polyhexes with n cells.

References

E. M. Palmer, Variations of the cell growth problem, Lect. Notes Math. 303 (1972), 215-224.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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..20.

A. T. Balaban, J. Brunvoll, B. N. Cyvin & S. J. Cyvin, Enumeration of branched catacondensed benzenoid hydrocarbons and their numbers of Kekulé structures Tetrahedron, 44(1) (1988), 221-228. See Table 1.

Wenchen He and Wenjie He, Generation and enumeration of planar polycyclic aromatic hydrocarbons, Tetrahedron 42.19 (1986): 5291-5299. See Table 1, column B.

Ed Pegg, Jr., Illustrations of polyforms

Eric Weisstein's World of Mathematics, Polyhex

Crossrefs

Cf. A323931, A323932.

Sequence in context: A000084 A057734 A151516 * A121186 A309505 A309504

Adjacent sequences: A003101 A003102 A003103 * A003105 A003106 A003107

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

a(8)-a(12) from Ed Pegg Jr, May 13 2009

a(13)-a(19) from Joseph Myers, Nov 26 2010

a(20) from Trinajstić et al. (Table 4.2, the number of cata-condensed benzenoids with h hexagons, unbranched) added by Andrey Zabolotskiy, Feb 08 2023

Status

approved