Some Addition Formulas for Fibonacci, Pell and Jacobsthal Numbers

• Autorzy: Göksal Bilgici , Tuncay Deniz Şentürk
• Języki publikacji: EN

Abstrakty

EN

In this paper, we obtain a closed form for $F_{\sum_{i=1}^k}, P_{\sum_{i=1}^k}$ and $J_{\sum_{i=1}^k}$ for some positive integers $k$ where $F_r$, $P_r$ and $J_r$ are the rth Fibonacci, Pell and Jacobsthal numbers, respectively. We also give three open problems for the general cases $F_{\sum_{i=1}^k}, P_{\sum_{i=1}^k}$ and $J_{\sum_{i=1}^k}$ for any arbitrary positive integer $n$.(original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical functions; Mathematical statistics; Number theory

PL

Matematyka; Funkcje matematyczne; Statystyka matematyczna; Teoria liczb

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2019
• Tom: 33
• Strony: 55--65

Twórcy

autor

Göksal Bilgici

• Kastamonu University Department of Computer Education and Instructional Technologies

autor

Tuncay Deniz Şentürk

• Kastamonu University Department of Mathematics, Institute of Science and Technology

Bibliografia

• H.W. Gould, A history of the Fibonacci Q-matrix and a higher-dimensional problem, Fibonacci Quart. 19 (1981), no. 3, 250-257.
• F. Koken and D. Bozkurt, On the Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sci. 3 (2008), no. 13, 605-614.
• T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.
• T. Koshy, Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
• P. Mana, Problem B-152: Fibonacci addition formula, Fibonacci Quart. 7 (1969), no. 3, 336.
• OEIS Foundation Inc., The On-Line Encyclopedia of Integer Sequences, 2011, http://oeis.org

Identyfikatory

DOI

10.2478/amsil-2019-0005