Van Der Laan Hibrit Dizileri Üzerine

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.