

A258012


Capped binary boundary codes for fusenes (all orientations and rotations included).


5



1, 127, 1519, 1783, 1915, 1981, 2014, 6007, 7099, 7645, 7918, 20335, 22447, 23479, 23503, 23995, 24187, 24253, 24286, 26551, 27607, 28123, 28135, 28381, 28477, 28510, 29659, 30187, 30445, 30451, 30574, 30622, 31213, 31477, 31606, 31609, 31990, 32122, 32188
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OFFSET

0,2


COMMENTS

Differs from A258002 for the first time at n=6622, where a(6622) = 69131119 which is missing from A258002 because that number codes for one of the 26 different orientations of the same 26edge sixhex polyhex where the two hexes at the ends of the pattern touch each other. This pattern is isomorphic to benzenoid [6]Helicene (up to chirality, see the illustrations at Wikipediapage).
The terms in this sequence are those whose binary representation can be rewritten to 127 (in binary "1111111", which encodes the boundary of a single hexagon) with an appropriate sequence of invocations of recurrences A254109 and A258009. However, there are some intricacies as how this should be done to get correct results. (Please see Kovič paper.)
Note that the papers in literature employ different, "Boundary Edges Code for Benzenoid Systems" (BEC for short) but to which these binary boundary codes can be directly related via their runlengths.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..20648
Guo, Hansen, Zheng, Boundary uniqueness of fusenes, Discrete Applied Mathematics 118 (2002), pp. 209222.
A. Karttunen, Related ideas coded in Prolog around 2004  2006 (at Internet Archive. Might contain a few erroneous definitions.)
Jurij Kovič, How to Obtain The Number of Hexagons in a Benzenoid System from Its Boundary Edges Code, MATCH Commun. Math. Comput. Chem. 72 (2014) pp. 2738.
Eric Weisstein's World of Mathematics, Fusene
Wikipedia, Helicene


EXAMPLE

8167737748888 is included in the sequence, as it encodes a 42edge polyhex pattern which is composed of two sevenhex "crowns" connected by a snakelike "Spiece".


CROSSREFS

Subsequences: A258002 (only strictly nonoverlapping codes, i.e., the holeless polyhexes), A258013 (only the lexicographically largest representatives from each equivalence class obtained by rotating).
Cf. A254109, A258009.
Sequence in context: A300339 A189026 A287653 * A258002 A025598 A115153
Adjacent sequences: A258009 A258010 A258011 * A258013 A258014 A258015


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, May 31 2015


STATUS

approved



