A258017 Number of one-sided fusenes (not necessarily planar) of perimeter 2n, counted up to rotations.

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

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, 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 A258013 with binary width = 2n + 1, or equally, with A000523(k) = 2n.

Links

Table of n, a(n) for n=1..13.

Xiaofeng Guo, Pierre Hansen, and Maolin Zheng, Boundary uniqueness of fusenes, Discrete Applied Mathematics 118 (2002), pp. 209-222.

Pornrat Ruengrot and Duangkamon Baowan, Classification of k-defect holes on a graphene sheet, Comp. Materials Sci. (2023) Vol. 225, 112181.

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: A370869 A209020 A258204 * A209055 A209212 A222847

Adjacent sequences: A258014 A258015 A258016 * A258018 A258019 A258020

Keyword

nonn,more

Author

Antti Karttunen, Jun 02 2015

Status

approved