Generalized Pierre Numbers

Abstract

In this paper, we introduce and investigate the generalized Pierre sequences for the first time and we deal with, in detail, two special cases, namely, Pierre and Pierre-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 Pierre, Pierre-Lucas and Tribonacci, Tribonacci-Lucas numbers