Certain classes of finite sums that involve generalized Fibonacci and Lucas numbers

@inproceedings{Melham2004CertainCO,
  title={Certain classes of finite sums that involve generalized Fibonacci and Lucas numbers},
  author={R. S. Melham},
  year={2004}
}
was the inspiration for [2], in which analogous sums involving cubes of Fibonacci numbers were developed. In turn, [2] was the motivation for [5], [6], and [7]. In the present paper, where we restrict ourselves to summands that consist of products of at most two terms (as in (1.1)), our motivation has again been to find sums where the right side has a pleasing form. We have found it profitable to consider non-alternating sums, alternating sums, and sums that 

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