Abstract
In this paper, a non-homogeneous version of the classical Fibonacci recurrence relation is investigated. The inhomogeneity is defined by a harmonic sequence , with real-valued parameters . It turns out that the golden ratio rule carries over to the solution of the non-homogeneous recurrence for almost all parameter values. The exceptional set is a one-dimensional submanifold in –-space, which is related to the graph of the Lerch transcendent.
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