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    On generalized Pentanacci quaternions
    (Tbilisi Centre Math Sci, 2020) Soykan, Yuksel; Ozmen, Nejla; Gocen, Melih
    In this paper, we introduce the generalized Pentanacci quaternions and we present Binet's formulas, generating functions and the summation formulas for these quaternions and as special case for Pentanacci and Pentanacci-Lucas quaternions. Furthermore, we present matrices related to generalized Pentanacci quaternions.
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    On properties of generalized Tridovan numbers
    (Bulgarian Acad Science, 2023) Soykan, Yuksel; Ozmen, Nejla; Okumus, Inci
    In this paper, we examine generalized Tridovan sequences and treat in detail two cases called Tridovan sequences and Tridovan-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. In addition, we give some identities and matrices related to these sequences.