Generalizations of Modified Pell and Pell-Lucas Sequences and Their Generating Matrices and Some Sums

Yıl 2016, Cilt: 9 Sayı: 3 - Cilt: 9 Sayı: 3, 178 - 184, 29.12.2016

Ahmet Daşdemir

Öz

This paper deals with the generalizations of the usual Modified Pell numbers and Pell-Lucas and an investigation of their certain identities. For this purpose, the generalized Modified Pell numbers and Pell-Lucas numbers are created, and appropriate initial conditions for them are presented. Some sum formulae consisting of the generalized Modified Pell numbers and Pell-Lucas numbers are investigated. A very fundamental features corresponding to these new generalizations are obtained by using matrix representations. Especially, an important relationship between the generalized Modified Pell and Pell-Lucas numbers is discovered.