Fibonacci-like sequence associated with k-Pell, k-Pell-Lucas and Modified k-Pell sequences

• Autorzy: Wani A. A. , Bhat S. A. , Rathore G. P. S.

Identyfikatory

DOI

10.17512/jamcm.2017.2.13

• Języki publikacji: EN

Abstrakty

EN

Fibonacci sequence is a well known example of second order linear recurrence relatio. Besides Fibonacci numbers and their generalizations have many applications as well as interesting properties almost in every field of science such as in Physics, Biology, Mathematics (Algebra, Geometry and Number Theory itself). The main aim of the present article to introduce a generalization of Fibonacci sequence which is similar to k-Pell, k-Pell-Lucas, Modified k-Pell sequences and known as Fibonacci-Like sequence. After that we obtain some fundamental properties of Fibonacci-Like sequence such as Binet formulae of Fibonacci-Like sequence, binomial transform of the Fibonacci-Like sequence and sum of Fibonacci-Like numbers with indexes in an arithmetic sequence. In addition to this we obtain some new relations among k-Pell, k-Pell-Lucas, Modified k-Pell and Fibonacci-Like sequences.

Słowa kluczowe

EN

k-Pell sequence; k-Pell-Lucas sequence; modified k-Pell sequence; generalized Fibonacci sequence

PL

uogólniony ciąg Fibonacciego; ciąg Fibonacciego; ciąg k-Pell; ciąg k-Pell-Lucas

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 2
• Strony: 159--171
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Wani A. A.

• School of Studies in Mathematics, Vikram University Ujjain, Ujjain, India

autor

Bhat S. A.

• Department of Mathematics, Aligarh Muslim University, India

autor

Rathore G. P. S.

• Department of Statistics, Horticulture College Mandsaur, Mandsaur India

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).