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A new family of Gauss (k, t) -Horadam numbersTaştan, MerveYllmaz, NazmiyeÖzkan, EnginCassini identityFibonacci numberGauss numbergenerating functionHoradam numberWe present a new family of Gauss (k,t)-Horadam numbers and obtain Binet formula of this family. We give the relationship between this family and the known Gauss t-Horadam number. Then we prove the Cassini and Catalan identities for this family. Furthermore, we investigate the sums, the recurrence relations and generating functions of this family. © 2022 World Scientific Publishing Company.World Scientific2022Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/12597https://doi.org/10.1142/s17935571225022541793-5571enAsian-European Journal of Mathematicsinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/12597