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Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers

Zvonko Čerin ; Kopernikova 7, 10020 Zagreb, Croatia

Puni tekst: engleski, pdf (189 KB) str. 1-12 preuzimanja: 693* citiraj
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. Preuzeto s 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. , br. 523=19, 2015, str. 1-12. https://hrcak.srce.hr/145093. Citirano 25.09.2021.
Chicago 17th Edition
Čerin, Zvonko. "Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers." Rad Hrvatske akademije znanosti i umjetnosti , br. 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), str. 1-12. Preuzeto s: https://hrcak.srce.hr/145093 (Datum pristupa: 25.09.2021.)
Vancouver
Čerin Z. Formulas for quadratic sums that involve generalized Fibonacci and Lucas numbers. Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 2015 [pristupljeno 25.09.2021.];(523=19):1-12. Dostupno na: 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., br. 523=19, str. 1-12, 2015. [Online]. Dostupno na: https://hrcak.srce.hr/145093. [Citirano: 25.09.2021.]

Sažetak
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.

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

Hrčak ID: 145093

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

Posjeta: 863 *