A Study on Generalized Blaise Numbers

Abstract

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