Irmak, NurettinSzalay, Laszlo2024-11-072024-11-0720121787-50211787-6117https://hdl.handle.net/11480/15373We apply a new approach, namely the fundamental theorem of homogeneous linear recursive sequences, to k-periodic binary recurrences which allows us to determine Binet's formula of the sequence if k is given. The method is illustrated in the cases k = 2 and k = 3 for arbitrary parameters. Thus we generalize and complete the results of Edson-Yayenie, and Yayenie linked to k = 2 hence they gave restrictions either on the coefficients or on the initial values. At the end of the paper we solve completely the constant sequence problem of 2-periodic sequences posed by Yayenie.eninfo:eu-repo/semantics/closedAccesslinear recurrencesk-periodic binary recurrencesArticle402535WOS:000434914300003N/A