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Number of C-rotamers with n carbon atoms.
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%I #15 Nov 20 2023 09:21:57

%S 1,1,1,3,7,25,95

%N Number of C-rotamers with n carbon atoms.

%C See Table 1 on page 3605 of Balaban and Schleyer paper.

%C a(n) counts free polysticks on the diamond net with n vertices. - _Andrey Zabolotskiy_, Nov 19 2023

%H A. T. Balaban, <a href="https://match.pmf.kg.ac.rs/electronic_versions/Match02/match2_51-61.pdf">Enumeration of Catafusenes, Diamond Hydrocarbons, and Staggered Alkane C-Rotamers</a>, MATCH Commun. Math. Comput. Chem., 2 (1976), 51-61.

%H A. T. Balaban and Paul von R. Schleyer, <a href="https://doi.org/10.1016/0040-4020(78)88437-3">Systematic classification and nomenclature of diamond hydrocarbons-I: Graph-theoretical enumeration of polymantanes</a>, Tetrahedron, (1978), vol. 34, pp. 3599 - 3609.

%e a(6) = 25 polysticks with 6 vertices include A038169(6) = 24 dual graphs to the hexagonal-face-connected animals formed by 6 triakis truncated tetrahedra (which are the Voronoi cells of the diamond net), including the 6-cycle, plus the 6-cycle without one edge.

%Y Cf. A038169, A039740.

%K nonn,more

%O 1,4

%A _Parthasarathy Nambi_, Aug 16 2006