In this paper, we investigate the generalized Pell-Padovan sequences and we deal with, in detail, four special cases, namely, Pell-Padovan, Pell-Perrin, third order Fibonacci-Pell and third order Lucas-Pell sequences. We present Binet’s formulas, generating functions, Simson formulas and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.
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Yüksel Soykan (2020) studied this question.