Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 94—103
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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.
- Fibonacci number
- Lucas number
- Sums of powers
2010 Mathematics Subject Classification
- Adegoke, K., Sums of fourth powers of Fibonacci and Lucas numbers, Preprint, May 2017, Available via arXiv.
- Adegoke, K., Factored closed-form expressions for the sums of cubes of Fibonacci and Lucas numbers, Preprint, June 2017, Available via arXiv.
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- Melham, R.S. (2000) Alternating sums of fourth powers of Fibonacci and Lucas numbers, The Fibonacci Quarterly, 38 (3), 254–259.
- Goy, T. & Shattuck, M. (2020). Fibonacci–Lucas identities and the generalized Trudi formula. Notes on Number Theory and Discrete Mathematics, 26 (3), 203-217, doi: 10.7546/nntdm.2020.26.3.203-217.
Cite this paper
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, doi: 10.7546/nntdm.2018.24.2.94-103.