On the Negatively Subscripted Padovan and Perrin Matrix Sequences

Nazmiye Yilmaz, Necati Taskara


The first main idea of this paper is to develop the matrix sequences that represent negatively subscripted Padovan and Perrin numbers. Then, by taking into account matrix properties for these new matrix sequences, some behaviours of negatively subscripted Padovan and Perrin numbers have been investigated. Moreover, we present the important relationships between negatively subscripted Padovan and Perrin matrix sequences.


Padovan matrix sequence; Perrin matrix sequence; generating function

Full Text:



H. Civciv and R. Türkmen, On the $(s, t)$-Fibonacci and Fibonacci matrix sequences, Ars Combinatoria 87 (2008), 161-173.

S. Falcon and A. Plaza, On the Fibonacci k-numbers, Chaos, Solitons & Fractal 32 (2007), 1615-1624.

H.H. Gulec and N. Taskara, On the $(s,t)$-Pell and $(s,t)$-Pell-Lucas sequences and their matrix representations, Applied Mathematics Letter 25 (2012), 1554-1559.

T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc, NY, 2001.

L. Marek-Crnjac, On the mass spectrum of the elementary particles of the standard model using El Naschies golden eld theory, Chaos, Solutions & Fractals 15(4) (2003), 611-618.

L. Marek-Crnjac, The mass spectrum of high energy elementary particles via El Naschies golden mean nested oscillators, the Dunkerly-Southwell eigenvalue theorems and KAM, Chaos, Solutions & Fractals 18(1) (2003), 125-133.

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 37(7) (2006), 825-831.

A.G. Shannon and A.F. Horadam, Generating functions for powers of third order recurrence sequences, Duke Mathematical Journal 38 (1971), 791-794.

N. Yilmaz and N. Taskara, Matrix sequences in terms of Padovan and Perrin numbers, Journal of Applied Mathematics, (2013), Article ID 941673.

Y. Yazlik, N. Taskara, K. Uslu and N. Yilmaz, The Generalized $(s,t)$-sequence and its matrix sequence, American Institute of Physics (AIP) Conf. Proc. 1389, (2012), 381-384.

Y. Yazlik and N. Taskara, A note on generalized k-Horadam sequence, Computers and Mathematics with Applications 63 (2012), 36-41.


  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905