cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A258018 #16 Feb 16 2025 08:33:25
%S A258018 0,0,1,0,1,1,3,1,8,5,20,11,62
%N A258018 Number of fusenes of perimeter 2n (not necessarily planar) with bilateral symmetry, counted up to rotations.
%C A258018 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.
%C A258018 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.
%H A258018 Guo, Hansen, Zheng, <a href="http://dx.doi.org/10.1016/S0166-218X(01)00180-9">Boundary uniqueness of fusenes</a>, Discrete Applied Mathematics 118 (2002), pp. 209-222.
%H A258018 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fusene.html">Fusene</a>
%H A258018 Wikipedia, <a href="http://en.wikipedia.org/wiki/Helicene">Helicene</a>
%F A258018 Other identities and observations. For all n >= 1:
%F A258018 a(n) = 2*A258019(n) - A258017(n).
%F A258018 a(n) >= A258205(n).
%Y A258018 Cf. A258017, A258019, A258204.
%Y A258018 Cf. A258015.
%K A258018 nonn,more
%O A258018 1,7
%A A258018 _Antti Karttunen_, Jun 02 2015