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

Author

Antti Karttunen, Jun 02 2015

Keywords

• nonn
• more

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

• Guo, Hansen, Zheng, Boundary uniqueness of fusenes, Discrete Applied Mathematics 118 (2002), pp. 209-222.
• Eric Weisstein's World of Mathematics, Fusene
• Wikipedia, Helicene

Crossrefs

Cf. A258017, A258019, A258204.

Cf. A258015.

Formula

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

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

a(n) >= A258205(n).