A Study on Generalized p-Oresme Numbers
Yüksel Soykan *
Department of Mathematics, Art and Science Faculty, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we introduce the generalized p-Oresme sequences and we deal with, in detail, three special cases which we call them modified p-Oresme, p-Oresme-Lucas and p-Oresme 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.
Keywords: Oresme numbers, Oresme-Lucas numbers, generalized Fibonacci numbers, modified p-Oresme numbers, p-Oresme-Lucas numbers, p-Oresme numbers