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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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