On the generalized Perrin and Cordonnier matrices

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  • Bartlett, C. and Huylebrouck D., Art and math of the 1:35 ratio rectangle, Symmetry: Culture and Science. 24(2013).
  • Brawer, R. and Pirovino M., The linear algebra of the Pascal matrix, Linear Algebra Appl. 174(1992), 13–23.
  • Cahill, N.D., D’Errico J.R., Narayan D.A. and Narayan J.Y., Fibonacci determinants, College Math. J. 33(2002), 221–225.
  • Gibson, P. M., An identity between permanents and determinants, Amer. Math. Monthly. 76(1969), 270–271.
  • Kaygisiz, K., Bozkurt D., k-Generalized Order-k Perrin Number Presentation by Matrix Method, Ars Combinatoria, 105(2012), 95-101.
  • Kaygisiz, K. and Sahin A., Generalized bivariate Lucas p-Polynomials and Hessenberg Ma- trices, J. Integer Seq. 15 Article 12.3.4.(2012).
  • Kaygisiz, K. and Sahin A., Determinant and permanent of Hessenberg matrix and generalized Lucas polynomials, Bull. Iranian Math. Soc. 39(6)(2013), 1065–1078.
  • Kaygisiz, K. and Sahin A., A new method to compute the terms of generalized order-k Fibonacci numbers, J. Number Theory. 133(2013), 3119–3126.
  • Kaygisiz, K. and Sahin A., Generalized Van der Laan and Perrin Polynomials, and Generaliza- tions of Van der Laan and Perrin Numbers, Selçuk Journal of Applied Math., 14(1)(2013),89- 103.
  • Kaygisiz, K. and Sahin A., Calculating terms of associated polynomials of Perrin and Cor- donnier numbers, Notes on Number Theory and Discrete Mathematics, 20(1)(2014),10-18.
  • Kilic, E. and Stakhov A.P., On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices, Chaos Solitons Fractals. 40(2009), 2210–2221.
  • Kilic, E. and Tasci D., The linear algebra of the Pell matrix, Bol. Soc. Mat. Mexicana. 2(11)(2005), 163-174.
  • Lee, G.Y., Kim J.S. and Lee S.G., Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart. 40(3)(2002), 203–211.
  • Lee, G.Y. and Kim J.S., The linear algebra of the k-Fibonacci matrix, Linear Algebra Appl. 373(2003), 75–87.
  • Li, H-C., On Fibonacci-Hessenberg matrices and the Pell and Perrin numbers, Appl. Math. Comput. 218(17)(2012), 8353–8358.
  • Li, H. and MacHenry T., Permanents and Determinants, Weighted Isobaric Polynomials, and Integer Sequences, Journal of Integer Sequences. 16 (2013)Article 13.3.5
  • Marohni´c, L. and Strmeµcki T., Plastic Number: Construction and Applications, Advanced Research in Scienti…c Areas. (3)7(2012), 1523-1528.
  • Minc, H. Encyclopedia of Mathematics and its Applications, Permanents, Vol.6, Addison- Wesley Publishing Company, 1978.
  • Ocal, A.A., Tuglu N. and Altinisik E., On the representation of k-generalized Fibonacci and Lucas numbers, Appl. Math. Comput. 170(1)(2005), 584–596.
  • Padovan, R., Dom Hans Van Der Laan and the Plastic Number, Nexus IV: Architecture and Mathematics, eds. Kim Williamsand Jose Francisco Rodrigues, Fucecchio (Florence): Kim Williams Books, 2002.
  • Padovan, R., Dom Hans van der Laan: Modern Primitive, Architectura Natura Press, 1994. [22] Shannon, A.G., Anderson P.G. and Horadam A. F., Properties of Cordonnier, Perrin and Van der Laan numbers. International Journal of Mathematical Education in Science and Technology. 37(2006), 825-831.
  • Sahin, A., On the Q analogue of …bonacci and lucas matrices and …bonacci polynomials, Utilitas Mathematica, 100(2016), 113–125.
  • Sahin, A. and Ramírez, J. R., Determinantal and permanental representations of convolved Lucas polynomials, Appl. Math. Comput., 281(2016), 314–322.
  • Yilmaz, F. and Bozkurt D., Hessenberg matrices and the Pell and Perrin numbers, J. Number Theory. 131(8)(2011),1390–1396.
  • Yilmaz, N. and Taskara N., Matrix Sequences in terms of Padovan and Perrin Numbers, Journal of Applied Mathematics (2013), Article ID 941673.