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_hz^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 _h of benzenoids of size h grows as h^2ν, with ν = 0.64115(5).