The one-dimensional, discrete Schr\"odinger equation is studied when the potential is allowed to take on two values, VA and VB, which are arranged according to a generalized Fibonacci sequence. The problem is reduced to a dynamical map for the traces of the transfer matrices which are given recursively by Mₗ₊₁=M_l-1{M}ₗⁿ$, where n is a positive integer. A related class of sequences whose transfer matrices obey the recursion formula ${M}ₗ₊₁$=${M}_{l{{-}}1}ⁿMₗ is also investigated.
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Gumbs et al. (1988) studied this question.
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