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We derive expressions for sums of first, second, third and fourth powers of Fibonacci and Lucas numbers and their alternating versions.On our way of exploration we rediscover some known results and present new.Focusing on third and fourth order power sums, our findings complete those of Clary and Hemenway, Melham and Adegoke.
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Baden-Wuerttemberg, L., & Frontczak, R. (2018). Sums of powers of Fibonacci and Lucas numbers: A new bottom-up approach. Notes on Number Theory and Discrete Mathematics, 24(2), 94–103. https://doi.org/10.7546/nntdm.2018.24.2.94-103
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