A Study on the Sums of Squares of Generalized Fibonacci Numbers: Closed Forms of the Sum Formulas Σn k=0 kxkW2 k and Σn k=1 kxkW2- k
Asian Journal of Advanced Research and Reports · pp. 44–67 · Published 9 Jul 2020
10.9734/ajarr/2020/v12i130280Abstract
In this paper, closed forms of the sum formulas Σn k=0 kxkW2 k and Σn k=1 kxkW2 -k for the squares of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery. Our work generalize second order recurrence relations.
Cited by 2
Related research
- Closed Formulas for the Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Σn k=0W3 Σ k and n k=1W3 — shares topic coverage
- Some Properties of Generalized Fibonacci Numbers: Identities, Recurrence Properties and Closed Forms of the Sum Formulas ∑nk=0 xkWmk+j — shares topic coverage
- On Summing Formulas for Horadam Numbers — shares topic coverage
- Closed Formulas for the Sums of Squares of Generalized Fibonacci Numbers — shares topic coverage
- On Summing Formulas for Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers — shares topic coverage
Article metrics
Real usage data collected on this platform.
0
Page views
0
PDF downloads
0
Outbound clicks
2
Citations
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
No views recorded yet.
Traffic sources
Referring site, by host.
No traffic recorded yet.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.