On Power Sums Involving Lucas Functions Sequences

摘要

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.