

A258017


Number of onesided fusenes (not necessarily planar) of perimeter 2n, counted up to rotations.


4



0, 0, 1, 0, 1, 1, 3, 3, 16, 23, 80, 183, 564
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OFFSET

1,7


COMMENTS

This sequence counts fusenes up to rotations, but with no turning over allowed. Fusenes are like polyhexes with additional criteria that no holes are allowed, while on the other hand, helicenelike selftouching or selfoverlapping configurations are included in the count here. Cf. the links and further comments at A258019.
For n >= 1, a(n) gives the total number of terms k in A258013 with binary width = 2n + 1, or equally, with A000523(k) = 2n.


LINKS

Table of n, a(n) for n=1..13.
Guo, Hansen, Zheng, Boundary uniqueness of fusenes, Discrete Applied Mathematics 118 (2002), pp. 209222.
Eric Weisstein's World of Mathematics, Fusene
Wikipedia, Helicene


FORMULA

Other identities and observations. For all n >= 1:
a(n) = 2*A258019(n)  A258018(n).
a(n) >= A258204(n).


CROSSREFS

Cf. A258018, A258019, A258204.
Cf. A258013.
Sequence in context: A292356 A209020 A258204 * A209055 A209212 A222847
Adjacent sequences: A258014 A258015 A258016 * A258018 A258019 A258020


KEYWORD

nonn,more


AUTHOR

Antti Karttunen, Jun 02 2015


STATUS

approved



