On Power Sums Involving Lucas Functions Sequences

الملخص EN

We present some general formulas related to sum of powers, also with alternating sign, involving Lucas functions sequences.

In particular, our formulas give a synthesis of various identities involving sum of powers of well-known polynomial sequences such as Fibonacci, Lucas, Pell, Jacobsthal, and Chebyshev polynomials.

Finally, we point out some interesting divisibility properties between polynomials arising from our results.