Sums of a polynomial times a Fibonacci-type recurrence term are shown to have one and only one representation as sequence terms at shifted indices plus a polynomial.
Nair, On weighted sums of Horadam numbers
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Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum
Sums of a polynomial times a Fibonacci-type recurrence term are shown to have one and only one representation as sequence terms at shifted indices plus a polynomial.