On the Number of Benzenoid Hydrocarbons

We present a new algorithm which allows a radical increase in the computer enumeration of benzenoids b _h with h hexagons. We obtain b _h up to h = 35. We prove that b _h ∼ const.κ ^h , prove the rigorous bounds 4.789 ≤ κ ≤ 5.905, and estimate that κ = 5.16193016(8). Finally, we provide strong numerical evidence that the generating function ∑b _h Z ^h ∼ A(Z) log(1 - κZ), estimate A(1/κ) and predict the subleading asymptotic behavior. We also provide compelling arguments that the mean-square radius of gyration 〈R _g ² 〉 _h of benzenoids of size h grows as h ^2ν , with ν = 0.64115(5).