Abstract. We present an improved parallel algorithm for the enumeration of fixed benzenoids B_h containing h hexagonal cells. We can thus extend the enumeration of B_h from the previous best h = 35 up to h = 50. Analysis of the associated generating function confirms to a very high degree of certainty that B_h~Aκ^h/h and we estimate that the growth constant κ = 5.161 930 154(8) and the amplitude A = 0.280 8499(1).

Key words: critical exponents and amplitudes (theory); series expansions

E-print number: 0808.0963
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Received 19 September 2008, accepted for publication 21 January 2009
Published 27 February 2009