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Y¨üksel Soykan

Publications (9)

A Study on Generalized Balancing Numbers

Y¨üksel Soykan · Asian Journal of Advanced Research and Reports · 2021

In this paper, we investigate properties of the generalized balancing sequence and we deal with, in detail, namely, balancing, modified Lucas-balancing and Lucas-balancing sequences. We present Binet’s formulas, generating functions and Simson formulas for these sequences. We als...

Open access Research Article 10.9734/ajarr/2021/v15i530401

Generalized Fibonacci Numbers with Indices in Arithmetic Progression and Sum of Their Squares: The Sum Formula ∑nk=0 xkW2mk+j

Y¨üksel Soykan · Journal of Advances in Mathematics and Computer Science · 2021

In this paper, closed forms of the sum formulas ∑n k=0 xkWmk 2 +j for 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 formu...

Open access Research Article 10.9734/jamcs/2021/v36i630371

A Study on Generalized Tetranacci Numbers: Closed Form Formulas ∑n k=0 xkWk2 of Sums of the Squares of Terms

Y¨üksel Soykan · Asian Research Journal of Mathematics · 2020

In this paper, closed forms of the sum formulas ∑n k=0 xkWk2 for the squares of generalized Tetranacci numbers are presented. We also present the sum formulas ∑n k=0 xkWk+1Wk; ∑n k=0 xkWk+2Wk; and ∑n k=0 xkWk+3Wk: As special cases, we give summation formulas of the of Tetranacci,...

Open access Research Article 10.9734/arjom/2020/v16i1030234

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

Y¨üksel Soykan · Asian Journal of Advanced Research and Reports · 2020

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 pr...

Open access Research Article 10.9734/ajarr/2020/v12i130280

A Study on Sum Formulas of Generalized Tetranacci Numbers: Closed Forms of the Sum Formulas \(\sum_{k=0}^{n}kW_{k}\) and \(\sum_{k=1}^{n}kW_{-k}\)

Y¨ uksel Soykan & Y¨üksel Soykan · Asian Journal of Advanced Research and Reports · 2021

In this paper, closed forms of the sum formulas \(\sum_{k=0}^{n}kW_{k}\) and \(\sum_{k=1}^{n}kW_{-k}\) for generalized Tetranacci numbers are presented. As special cases, we give summation formulas of Tetranacci, Tetranacci-Lucas, and other fourth-order recurrence sequences.

Open access Research Article 10.9734/ajarr/2021/v15i130359