On Generalized Third-Order Jacobsthal Numbers

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.