De Moivre-Type Identities for the Padovan Numbers

Abstract

At this work, we give a method for constructing the Perrin and Padovan sequences and obtain the De Moivre-type identity for Padovan numbers. Also, we define a Padovan sequence with new initial conditions and find some identities between all of these auxiliary sequences. Furthermore, we give quadratic approximations for these sequences.

Keywords

• De Moivre-type identity
• Padovan numbers
• Perrin numbers
• quadratic approximation

References

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