A258018 Number of fusenes of perimeter 2n (not necessarily planar) with bilateral symmetry, counted up to rotations.

0, 0, 1, 0, 1, 1, 3, 1, 8, 5, 20, 11, 62

Offset

1,7

Comments

This sequence counts fusenes which stay the same when flipped over. Fusenes are like polyhexes with additional criteria that no holes are allowed, but on the other hand, helicene-like self-touching or self-overlapping 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 A258015 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. 209-222.

Eric Weisstein's World of Mathematics, Fusene

Wikipedia, Helicene

Formula

Other identities and observations. For all n >= 1:

a(n) = 2*A258019(n) - A258017(n).

a(n) >= A258205(n).

Crossrefs

Cf. A258017, A258019, A258204.

Cf. A258015.

Sequence in context: A209136 A206800 A258205 * A188939 A062196 A103247

Adjacent sequences: A258015 A258016 A258017 * A258019 A258020 A258021

Keyword

nonn,more

Author

Antti Karttunen, Jun 02 2015

Status

approved