The New Members of Pell Sequence
Hasan Gökbaş *
Department of Mathematics, Faculty of Science and Literature, University of Bitlis Eren, Bitlis-13000, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this study, we define a new type of number sequence is called the alternative Pell and alternative Pell-Lucas sequences. These numbers are introduced from the characteristic equation families of Pell and Pell-Lucas numbers. We obtain the Binet’s formula, generating function formula, Tagiuri’s identity, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity, Vajda’s identity, Honsberger’s identity and some formulas for this new type numbers. Morever, we give the matrix representation of the alternative Pell and alternative Pell-Lucas numbers. We have also given the connection of these new number sequences with the silver ratio.
Keywords: Pell number, Pell-Lucas number, alternative Pell number, alternative Pell-Lucas number