A323931 Unbranched catacondensed benzenoids (strip polyhexes), mirror-symmetrical.

0, 0, 1, 1, 4, 3, 12, 10, 34, 28, 97, 81, 271, 226, 764, 638, 2141, 1787, 6025, 5030, 16924, 14116, 47623, 39727, 133934, 111655, 377003, 314297, 1061064, 884199

Offset

1,5

Links

Table of n, a(n) for n=1..30.

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) (1988), 221-228. See Table 1.

Björg N. Cyvin, Jon Brunvoll and Sven J. Cyvin, Enumeration of benzenoid systems and other polyhexes, p. 65-180 in: I. Gutman (ed.), Advances in the Theory of Benzenoid Hydrocarbons II, Springer, 1992.

Eric Weisstein's World of Mathematics, Polyhex.

Example

For n = 4, there are A003104(4) = 4 strip polyhexes, which Weisstein calls bar, worm, arch, and wave. The arch has mirror symmetry, it is counted by a(4) = 1. The worm is unsymmetric, it is counted by A323932(4) = 1. The wave has rotational symmetry. The bar has higher symmetry and is not counted by this sequence.

Crossrefs

The main sequences listed in Table 1 of Balaban et al. (1988) are A323931, A323932, A003104, A323851, A038142.

Sequence in context: A162766 A122804 A122544 * A205371 A270633 A272220

Adjacent sequences: A323928 A323929 A323930 * A323932 A323933 A323934

Keyword

nonn,more

Author

N. J. A. Sloane, Feb 09 2019

Extensions

a(13)-a(30) from Cyvin, Brunvoll & Cyvin (Tables 14 & 15) added by Andrei Zabolotskii, Feb 16 2023

Name corrected by Andrei Zabolotskii, Apr 03 2026

Status

approved