Generalized Adrien Numbers

Abstract

In this paper, we introduce and investigate the generalized Adrien sequences and we deal with, in detail, two special cases, namely, Adrien and Adrien-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between Adrien, Adrien-Lucas and third order Pell, third order Pell-Lucas numbers.