A258018 - OEIS

%I #15 Jun 13 2015 09:31:25

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

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

%C 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 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fusene.html">Fusene</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Helicene">Helicene</a>

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

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

%F a(n) >= A258205(n).

%Y Cf. A258017, A258019, A258204.

%Y Cf. A258015.

%K nonn,more

%O 1,7

%A _Antti Karttunen_, Jun 02 2015