Generalized Olivier Numbers
Asian Research Journal of Mathematics · pp. 1–22 · Published 2 Jan 2023
10.9734/arjom/2023/v19i1634Abstract
In this paper, we introduce and investigate the generalized Olivier sequences and we deal with, in detail, two special cases, namely, Olivier and Olivier-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. We also provide various matrices and identities associated with these sequences. Furthermore, we show that there are close relations between Olivier, Olivier-Lucas and adjusted Pell-Padovan, third order Lucas-Pell, third order Fibonacci-Pell, Pell-Perrin, Pell-Padovan numbers. Moreover, we give some identities and matrices related with these sequences.
Cited by 5
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