De Moivre-Type Identities for the Pell Numbers

Abstract

This paper aims to present a method for constructing the second order Pell and Pell-Lucas numbers and the third order Pell and Pell-Lucas numbers. Moreover, we obtain the De Moivre-type identities for these numbers. In addition, we define a Pell sequence with new initial conditions and give some identities for these third order Pell numbers such as Binet's formulas, generating functions, sums.

Keywords

• Pell numbers
• Pell-Lucas numbers
• De Moivre-type identity
• binet

References

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