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A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

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  • Hasan GökbaÅŸ

Abstract

In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a determinantal representation for the generating function of this sequence. We also provide some properties of these numbers. Moreover, we give the matrix representation of the biperiodic Leonardo numbers.

Suggested Citation

  • Hasan GökbaÅŸ, 2025. "A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence," Journal of Mathematics, Hindawi, vol. 2025, pages 1-9, March.
    • Handle: RePEc:hin:jjmath:3399017
    DOI: 10.1155/jom/3399017
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