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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 497418, 7 pages
Binomial Transforms of the Padovan and Perrin Matrix Sequences
Department of Mathematics, Faculty of Science, Selcuk University, Campus, 42075 Konya, Turkey
Received 18 July 2013; Accepted 13 September 2013
Academic Editor: Beong In Yun
Copyright © 2013 Nazmiye Yilmaz and Necati Taskara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- S. Falcón and A. Plaza, “On the Fibonacci -numbers,” Chaos, Solitons & Fractals, vol. 32, no. 5, pp. 1615–1624, 2007.
- T. Koshy, Fibonacci and Lucas Numbers with Applications, Pure and Applied Mathematics, Wiley-Interscience, New York, NY, USA, 2001.
- A. G. Shannon, P. G. Anderson, and A. F. Horadam, “Properties of Cordonnier, Perrin and Van der Laan numbers,” International Journal of Mathematical Education in Science and Technology, vol. 37, no. 7, pp. 825–831, 2006.
- Y. Yazlik and N. Taskara, “A note on generalized -Horadam sequence,” Computers & Mathematics with Applications, vol. 63, no. 1, pp. 36–41, 2012.
- L. Marek-Crnjac, “On the mass spectrum of the elementary particles of the standard model using El Naschie's golden field theory,” Chaos, Solutions & Fractals, vol. 15, no. 4, pp. 611–618, 2003.
- L. Marek-Crnjac, “The mass spectrum of high energy elementary particles via El Naschie’s golden mean nested oscillators, the Dunkerly-Southwell eigenvalue theorems and KAM,” Chaos, Solutions & Fractals, vol. 18, no. 1, pp. 125–133, 2003.
- H. Civciv and R. Türkmen, “On the -Fibonacci and Fibonacci matrix sequences,” Ars Combinatoria, vol. 87, pp. 161–173, 2008.
- H. H. Gulec and N. Taskara, “On the -Pell and -Pell-Lucas sequences and their matrix representations,” Applied Mathematics Letters, vol. 25, no. 10, pp. 1554–1559, 2012.
- Y. Yazlik, N. Taskara, K. Uslu, and N. Yilmaz, “The generalized (s, t)-sequence and its matrix sequence,” AIP Conference Proceedings, vol. 1389, pp. 381–384, 2012.
- N. Yilmaz and N. Taskara, “Matrix sequences in terms of Padovan and Perrin numbers,” Journal of Applied Mathematics. In press.
- K.-W. Chen, “Identities from the binomial transform,” Journal of Number Theory, vol. 124, no. 1, pp. 142–150, 2007.
- S. Falcon and A. Plaza, “Binomial transforms of k-Fibonacci sequence,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 11-12, pp. 1527–1538, 2009.
- H. Prodinger, “Some information about the binomial transform,” The Fibonacci Quarterly, vol. 32, no. 5, pp. 412–415, 1994.