OFFSET
1,7
COMMENTS
A fusene is a benzenoid (a polyhex) which has a single component of boundary edges (that is, no holes). Including also geometrically nonplanar configurations allows helicene-like self-touching or self-overlapping structures. Thus this sequence differs from A258206 for the first time at n=13 as here a(13) = 313 [while A258206(13) = 312] because the smallest such nonplanar structure is 26-edge [6]Helicene, which is encoded by one-capped binary code 131821024 (= A258013(875) = A258015(113)). Please see the illustrations at the Wikipedia page. Note that although in their three-dimensional conformation molecules like [6]Helicene and other [n]Helicenes with n >= 6 have two different chiralities (resulting from the handedness of the helicity itself), in this count of abstract combinatorial objects they are considered achiral because of their bilateral symmetry.
If one counts these structures by the number of hexes (instead of perimeter length), one obtains sequence 1, 1, 3, 7, 22, 82, ... (probably A108070).
LINKS
Guo, Hansen, Zheng, Boundary uniqueness of fusenes, Discrete Applied Mathematics 118 (2002), pp. 209-222.
Eric Weisstein's World of Mathematics, Fusene
Wikipedia, Helicene
FORMULA
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Antti Karttunen, Jun 02 2015
STATUS
approved