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Original scientific paper

Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers

Zvonko Čerin ; Kopernikova 7, 10020 Zagreb, Croatia

Fulltext: english, pdf (189 KB) pages 1-12 downloads: 693* cite
APA 6th Edition
Čerin, Z. (2015). Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers. Rad Hrvatske akademije znanosti i umjetnosti, (523=19), 1-12. Retrieved from https://hrcak.srce.hr/145093
MLA 8th Edition
Čerin, Zvonko. "Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers." Rad Hrvatske akademije znanosti i umjetnosti, vol. , no. 523=19, 2015, pp. 1-12. https://hrcak.srce.hr/145093. Accessed 20 Sep. 2021.
Chicago 17th Edition
Čerin, Zvonko. "Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers." Rad Hrvatske akademije znanosti i umjetnosti , no. 523=19 (2015): 1-12. https://hrcak.srce.hr/145093
Harvard
Čerin, Z. (2015). 'Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers', Rad Hrvatske akademije znanosti i umjetnosti, (523=19), pp. 1-12. Available at: https://hrcak.srce.hr/145093 (Accessed 20 September 2021)
Vancouver
Čerin Z. Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers. Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 2015 [cited 2021 September 20];(523=19):1-12. Available from: https://hrcak.srce.hr/145093
IEEE
Z. Čerin, "Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers", Rad Hrvatske akademije znanosti i umjetnosti, vol., no. 523=19, pp. 1-12, 2015. [Online]. Available: https://hrcak.srce.hr/145093. [Accessed: 20 September 2021]

Abstracts
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 (-1)^n(n+1)/2 it is possible to get similar formulas for the alternation according to the numbers (-1)^n(n-1)/2. We also consider twelve quadratic sums with binomial coefficients that are products.

Keywords
(generalized) Fibonacci number; (generalized) Lucas number; factor; sum; alternating; binomial coefficient; product

Hrčak ID: 145093

URI
https://hrcak.srce.hr/145093

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