A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Hasan Gökbaş

Journal of Mathematics, 2025, vol. 2025, 1-9

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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3399017

DOI: 10.1155/jom/3399017

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