**Abstract.** We improve on Melham’s formulas in [10, Section 4] for
certain classes of finite sums that involve generalized Fibonacci and Lucas
numbers. Here we study the quadratic sums where products of two of these
numbers appear. Our results show that most of his formulas are the initial
terms of a series of formulas, that the analogous and somewhat simpler
identities hold for associated dual numbers and that besides the alternation
according to the numbers ^{n(n+1)/2}^{n(n-1)/2}.

**2010 Mathematics Subject Classification.**
11B39, 11Y55, 05A19.

**Key words and phrases.** (generalized) Fibonacci number, (generalized) Lucas number,
factor, sum, alternating, binomial coefficient, product.

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MathSciNet