On a New one Parameter Generalization of Pell Numbers

• Autorzy: Dorota Bród
• Języki publikacji: EN

Abstrakty

EN

In this paper we present a new one parameter generalization of the classical Pell numbers. We investigate the generalized Binet's formula, the generating function and some identities for $r$-Pell numbers. Moreover, we give a graph interpretation of these numbers.(original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical statistics; Mathematical functions

PL

Matematyka; Statystyka matematyczna; Funkcje matematyczne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2019
• Tom: 33
• Strony: 66--76

Twórcy

autor

Dorota Bród

• Politechnika Rzeszowska im. Ignacego Łukasiewicza Wydział Matematyki i Fizyki Stosowanej

Bibliografia

• P. Catarino, On some identities and generating functions for k-Pell numbers, Int. J. Math. Anal. (Ruse) 7 (2013), no. 38, 1877-1884.
• P. Catarino and P. Vasco, Some basic properties and a two-by-two matrix involving the k-Pell numbers, Int. J. Math. Anal. (Ruse) 7 (2013), no. 45, 2209-2215.
• R. Diestel, Graph Theory, Springer-Verlag, Heidelberg-New York, 2005.
• A.F. Horadam, Pell identities, Fibonacci Quart. 9 (1971), no. 3, 245-252, 263.
• E.G. Kocer and N. Tuglu, The Binet formulas for the Pell and Pell-Lucas p-numbers, Ars Combin. 85 (2007), 3-17.
• K. Piejko and I. Włoch, On k-distance Pell numbers in 3-edge coloured graphs, J. Appl. Math. 2014, Art. ID 428020, 6 pp.
• H. Prodinger and R.F. Tichy, Fibonacci numbers of graphs, Fibonacci Quart. 20 (1982), no. 1, 16-21.
• S.Wagner and I. Gutman, Maxima and minima of the Hosoya index and the Merrifield-Simmons index: a survey of results and techniques, Acta Appl. Math. 112 (2010), no. 3, 323-346.
• A. Włoch and I. Włoch, Generalized Pell numbers, graph representations and independent sets, Australas. J. Combin. 46 (2010), 211-215.

Identyfikatory

DOI

10.2478/amsil-2019-0011