On the bi-periodic Padovan sequences

Abstract

In this study, we define a new generalization of the Padovan numbers, which shall also be called the bi-periodic Padovan sequence. Also, we consider a generalized bi-periodic Padovan matrix sequence. Finally, we investigate the Binet formulas, generating functions, series and partial sum formulas for these sequences.

Keywords

• padovan sequence
• binet-like formula
• generating function
• biperiodic padovan sequence
• matrix