A258017 - OEIS

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

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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, 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