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On the properties of iterated binomial transforms for the Padovan and Perrin matrix sequences. (English) Zbl 1367.11027
Summary: In this study, we apply “\(r\)” times the binomial transform to the Padovan and Perrin matrix sequences (for definitions see the authors [“Matrix sequences in terms of Padovan and Perrin numbers”, J. Appl. Math. 2013, Art. ID 941673, 7 p. (2013; doi:10.1155/2013/941673)]). Also, the Binet formulas, summations, generating functions of these transforms are found using recurrence relations. Finally, we give the relationships of between iterated binomial transforms for Padovan and Perrin matrix sequences.

MSC:
11B65 Binomial coefficients; factorials; \(q\)-identities
11B83 Special sequences and polynomials
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