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Binomial transforms of the Padovan and Perrin matrix sequences. (English) Zbl 1294.11012
Summary: We apply the binomial transforms to Padovan and Perrin matrix sequences. Also, the Binet formulas, summations, and generating functions of these transforms are found by recurrence relations. Finally, we illustrate the relations between these transforms by deriving new formulas.

##### MSC:
 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11B75 Other combinatorial number theory
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##### References:
 [1] Falcón, S.; Plaza, A., On the Fibonacci $$k$$-numbers, Chaos, Solitons & Fractals, 32, 5, 1615-1624, (2007) · Zbl 1158.11306 [2] Koshy, T., Fibonacci and Lucas Numbers with Applications. Fibonacci and Lucas Numbers with Applications, Pure and Applied Mathematics, xviii+652, (2001), New York, NY, USA: Wiley-Interscience, New York, NY, USA · Zbl 0984.11010 [3] Shannon, A. G.; Anderson, P. G.; Horadam, A. F., Properties of Cordonnier, Perrin and Van der Laan numbers, International Journal of Mathematical Education in Science and Technology, 37, 7, 825-831, (2006) · Zbl 1149.11300 [4] Yazlik, Y.; Taskara, N., A note on generalized $$k$$-Horadam sequence, Computers & Mathematics with Applications, 63, 1, 36-41, (2012) · Zbl 1238.11015 [5] Marek-Crnjac, L., On the mass spectrum of the elementary particles of the standard model using El Naschie’s golden field theory, Chaos, Solutions & Fractals, 15, 4, 611-618, (2003) · Zbl 1033.81521 [6] Marek-Crnjac, L., The mass spectrum of high energy elementary particles via El Naschie’s $$E^{(\infty)}$$ golden mean nested oscillators, the Dunkerly-Southwell eigenvalue theorems and KAM, Chaos, Solutions & Fractals, 18, 1, 125-133, (2003) [7] Civciv, H.; Türkmen, R., On the $$(s, t)$$-Fibonacci and Fibonacci matrix sequences, Ars Combinatoria, 87, 161-173, (2008) · Zbl 1224.11015 [8] Gulec, H. H.; Taskara, N., On the $$(s, t)$$-Pell and $$(s, t)$$-Pell-Lucas sequences and their matrix representations, Applied Mathematics Letters, 25, 10, 1554-1559, (2012) · Zbl 1246.11031 [9] Yazlik, Y.; Taskara, N.; Uslu, K.; Yilmaz, N., The generalized (s, t)-sequence and its matrix sequence, AIP Conference Proceedings, 1389, 381-384, (2012) [10] Yilmaz, N.; Taskara, N., Matrix sequences in terms of Padovan and Perrin numbers · Zbl 1397.15038 [11] Chen, K.-W., Identities from the binomial transform, Journal of Number Theory, 124, 1, 142-150, (2007) · Zbl 1120.05007 [12] Falcon, S.; Plaza, A., Binomial transforms of k-Fibonacci sequence, International Journal of Nonlinear Sciences and Numerical Simulation, 10, 11-12, 1527-1538, (2009) [13] Prodinger, H., Some information about the binomial transform, The Fibonacci Quarterly, 32, 5, 412-415, (1994) · Zbl 0818.05002
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