Unrestricted Pell and Pell – Lucas 2N-ons

Authors : Öznur BAYRAKÇI ÖZSOY, Göksal BİLGİCİ

Pages : 112-116

Doi:10.34088/kojose.1033409

View : 16 | Download : 11

Publication Date : 2022-11-30

Article Type : Research Paper

Abstract :In this study, we define unrestricted Pell and Pell – Lucas hyper-complex numbers. We choose arbitrary Pell and Pell – Lucas numbers for the coefficients of the ordered basis 〖{e〗_0,e_1,⋯,e_insert ignore into journalissuearticles values(N-1);} of hyper-complex 2^N-ons where N∈{0,1,2,3,4} and call these hyper-complex numbers unrestricted Pell and Pell-Lucas 2N-ons. We give generating functions and Binet formulas for these type of hyper-complex numbers. We also obtain some generalization of well – known identities such as Catalan’s, Cassini’s and d’Ocagne’s identities.
Keywords : Pell sequence, Pell Lucas sequence, Quaternion, Octonion, Sedenion