文摘
A Möbius type cyclic polyazulenoid is a kind of nonalternant conjugated hydrocarbon, consisting of a cyclic series of alternatingly fused five membered rings and seven membered rings, which forms a “Möbius belt of rings” or say, “Möbius belt of azulenes”, more precisely. As a sequel of the recent paper (Deng and Zhang in J Math Chem 54(2):416–427, 2016), which counts “belt type” cyclic polyazulenoid, this article studies the enumeration problem of Möbius type cyclic polyazulenoid. We obtain the exact counting formula for the number of Möbius type cyclic polyazulenoids with n azulene units, by a method based on coding technique and a generalization of ‘Burnside’ lemma. And we give the numerical results for n not larger than 20, which may contribute to the fully synthesis of Möbius type cyclic polyazulenoids.