Using the extended real-space renormalizaation-group approach, we study the local electr-onic properties of a class of one-dimensional quasicrystals (the generalized Fibonacci chains) in the framework of tight-binding model. These quasiperiodic systems are termed the An chains, which are associated with the sequences generated by the inflation rule (A, B)→(AnB, A). We introduce 2n2+1 transformations for calculating the local electronic Green's function and the local electronic density of state at any site in any one of An chains for the diagonal, offdiago-nal and combined models. It is shown that this approach is effective and the local electronic density of states is critical, just as that of Fibonacci quasicrystal.
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