on the Van Der Laan hybrid sequence

Öz

Many authors studied special recursion sequences such as Pell sequence, Pell Lucas sequence, Padovan and Perrin sequences, Jacobsthal sequence. They established new results about these sequences. Ozdemir (2018) introduced the hybrid numbers as a generalization of complex hyperbolic and dual numbers. The set H of hybrid numbers Z is of the form Z=a+bi+cϵ+dh, Where a,b,c∈R and i,ϵ,h are operators such that i^2=-1 ,ϵ^2=0,ih=-hi= ϵ+i. For more results about the hybrid number we refer to (Ozdemir, 2018). The conjugate of hybrid number Z is defined by ¯Z=¯(a+bi+cϵ+dh)=a-bi-cϵ-dh . Liana and Wloch (2019) introduced the Jacobsthal and Jacobsthal Lucas hybrid numbers and investigated some of their properties. In this paper we introduce the Van Der Laan hybrid sequence. We obtain Binet-like formula of this sequence. Then we represent the partial sum and generating function of this sequence. We study some properties of this sequence. Finally we find the eigenvalues and determinant of particular circulant matrix involving van Der Laan hybrid sequence.

Anahtar Kelimeler

• Van der Laan sequence
• hybrid numbers
• partial sum
• generating function
• determinant

Van Der Laan Hibrit Dizileri Üzerine

Öz

Bu makalede Van Der Laan hibrit dizisi tanıtıldı. Bu dizi ile ilişkili Binet benzeri formül, kısmi toplam ve üreteç fonksiyonu elde edildi. Van Der Laan hibrit dizisinin bazı ilginç özellikleri verildi. Son olarak, Van Der Laan hibrit dizisini içeren bir sirkülant matrisin öz değerleri ve determinantı sunuldu.

Anahtar Kelimeler

• Van Der Laan dizisi
• hibrit sayılar
• kısmi toplam
• üreteç fonksiyonu
• determinant.
• Van Der Laan dizisi, hibrit sayılar, kısmi toplam, üreteç fonksiyonu, determinant.

Teşekkür

Thanks the referees for their significant statements about the paper.

Kaynakça

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