On Generalized Third-Order Jacobsthal Numbers
Evren Eyican Polatlı *
Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey.
Yüksel Soykan
Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we investigate the generalized third order Jacobsthal sequences and we deal with, in detail, four special cases, namely, third order Jacobsthal, third order Jacobsthal-Lucas, modified third order Jacobsthal, third order Jacobsthal Perrin 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: Jacobsthal numbers, third order Jacobsthal numbers, third order Jacobsthal-Lucas, third order Jacobsthal Perrin numbers