In this paper, we consider a generalization of Horadam sequence $\left\{w_{n}\right\} $ which is defined by the recurrence $w_{n}=aw_{n-1}+cw_{n-2},$ if $n$ is even, $w_{n}=bw_{n-1}+cw_{n-2},$ if $n$ is odd with arbitrary initial conditions $w_{0},w_{1}$ and nonzero real numbers $a,b,$ and $c.$ We investigate some congruence properties of the generalized Horadam sequence $\{ w_{n}\}$.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this paper, we consider a generalization of Horadam sequence $\left\{w_{n}\right\} $ which is defined by the recurrence $w_{n}=aw_{n-1}+cw_{n-2},$ if $n$ is even, $w_{n}=bw_{n-1}+cw_{n-2},$ if $n$ is odd with arbitrary initial conditions $w_{0},w_{1}$ and nonzero real numbers $a,b,$ and $c.$ We investigate some congruence properties of the generalized Horadam sequence $\{ w_{n}\}$.
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Temel Bulgular & Veri:In this paper, we consider a generalization of Horadam sequence $\left\{w_{n}\right\} $ which is defined by the recurrence $w_{n}=aw_{n-1}+cw_{n-2},$ if $n$ is even, $w_{n}=bw_{n-1}+cw_{n-2},$ if $n$ is odd with arbitrary initial conditions $w_{0},w_{1}$ and nonzero real numbers $a,b,$ and $c.$ We investigate some congruence properties of the generalized Horadam sequence $\{ w_{n}\}$.
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Sonuç & Katkı:In this paper, we consider a generalization of Horadam sequence $\left\{w_{n}\right\} $ which is defined by the recurrence $w_{n}=aw_{n-1}+cw_{n-2},$ if $n$ is even, $w_{n}=bw_{n-1}+cw_{n-2},$ if $n$ is odd with arbitrary initial conditions $w_{0},w_{1}$ and nonzero real numbers $a,b,$ and $c.$ We investigate some congruence properties of the generalized Horadam sequence $\{ w_{n}\}$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Horadam sequence · generalized Fibonacci sequence · generalized Lucas sequence
Abstract
In this paper, we consider a generalization of Horadam sequence $\left\{w_{n}\right\} $ which is defined by the recurrence $w_{n}=aw_{n-1}+cw_{n-2},$ if $n$ is even, $w_{n}=bw_{n-1}+cw_{n-2},$ if $n$ is odd with arbitrary initial conditions $w_{0},w_{1}$ and nonzero real numbers $a,b,$ and $c.$ We investigate some congruence properties of the generalized Horadam sequence $\{ w_{n}\}$.
Tan, E., Leung, H. H. (2022). A note on congruence properties of the generalized bi-periodic Horadam sequence. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 6, 2084–2093. https://ajindex.com/articles/529659
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