Citations of

(with J.D. Louck) The combinatorial power of the companion matrix, Linear Algebra and Its Applications, 232 (1996) 261¨C278.


  1. B. Bernoussi, M. Rachidi and O. Saeki, Extending the Bernoulli-Euler method for finding zeros of holomorphic functions, Fibonacci Quart., 42 (2004) 55-65.

  2. Szu-En Cheng, Generating Function Proofs of Identities and Congruences, PhD Thesis, Michigan State University. 2003.

  3. W. S. Chou, Leetsch C. Hsu, and Peter J. S. Shiue, Application of Fa¨¤ di Bruno's formula in characterization of inverse relations, J. Comput. Appl. Math., 190 (2006) 151--169.

  4. B. S. Du, S. S. Huang and M. C. Li, Generalized Fermat, double Fermat and Newton sequences, J. Number Theory, 98 (2003) 172¨C183.

  5. Tian-Xiao He and Peter J.-S. Shiue, On sequences of numbers and polynomials defined by linear recurrence relations of order 2, International Journal of Mathematics and Mathematical Sciences 2009.

  6. Q. H. Hou and Y. P. Mu, Recurrent sequences and Schur functions, Adv. in Appl. Math., 31 (2003) 150-162.

  7. E. Kilic, The Binet formula, sums and representations of generalized Fibonacci p-numbers, European J. Combin, 29(2008)701¨C711.

  8. E. Kilic, The generalized order-k Fibonacci¨CPell sequence by matrix methods, J. Comput.Appl.Math., 209 (2007) 133 -145.

  9. E. Kilic and P. Stanica, Generating matrices for weighted sums of second order linear recurrences, J.Integer Seq., 12 (2009).

  10. E. Kilic, The generalized Pell (p, i)-numbers and their Binet formulas, combinatorial representations, sums, Chaos Solitons Fractals, 40 (2009) 2047-2063.

  11. E. Kilic, Sums of the squares of terms of sequence {un}, Proc. Indian Acad. Sci. (Math. Sci.), 118(2008) 27-41.

  12. E. Kilic, The generalized Fibonomial matrix, European J. Combin., 31 (2010) 193-209.

  13. E. Kilic, Tribonacci sequences with certain indices and their sums, Ars Combinatoria 86 (2008) 13-22.

  14. Emrah Kili? and Dursun Tasci, The generalized Binet formula, representation and sums of the generalized order-k Pell numbers, Taiwanese J. Math., 10 (6) (2006) 1661-1670.

  15. G. Y. Lee, J. S. Kim and S. G. Lee, A representation and some properties for k-Fibonacci sequences, Missouri J. Math. Sci., 13(2001) 92-102.

  16. G. Y. Lee, S. G. Lee, J. S. Kim and H. K. Shin, The Binet formula and representations of k-generalized Fibonacci numbers, Fibonacci Quart., 39 (2001) 158-164.

  17. A.Lim, J. Dai, On the product of companion matrics, Linear Algebra and its Applications, 435(2011), 2921-2935.

  18. R. K. Mallik, On the solution of a linear homogeneous difference equation with variable coefficients, SIAM J. Math. Anal., 31 (2000) 375-385.

  19. R. K. Mallik, Solutions of linear difference equations with variable-coefficients, J. Math. Anal. Appl., 222 (1998) 79-91.

  20. J. Abderram¨¢n Marrero, M. Rachidi, Application of the companion factorization to linear non-autonomous area-preserving maps, Linear and Miltilinear Algebra, 2011,1-17.

  21. L. Verde-Star, Functions of matrices, Linear Algebra Appl., 406 (2005) 285--300.

  22. V. Rovenski, P. Walczak, Extrinsic geometric flows on foliated manifolds, I, arxiv:math.Co/1003.1607v3.

  23. S. Jaroslav, Some quantities related to the distance matrix of a special type of digraphs, 3£¨2010£©2£¬249-256.

  24. S. Jaroslav, T. Pavel, Some properties of directed graphs corresponding to the companion matrix, Jounal of applied mathmatics, 2£¨2009£©1£¬55-64.

  25. R. B. Taher and M. Rachidi, On the matrix powers and exponential by the r-generalized Fibonacci sequences methods: the companion matrix case, Linear Algebra Appl., 370 (2003) 341-353.

  26. Sheng-liang Yang, On the k-generalized Fibonacci numbers and high-order linear recurrence relations, Appl. Math. Comput., 196 (2008) 850-857.

  27. Sheng-Liang Yang, On the k-generalized Lucas numbers, International Journal of Pure and Applied Mathematics, 21(2005)3, 293-297.

  28. Z. Z. Zhang and T. M. Wang, Generalized Pascal matrix and recurrence sequences, Linear Algebra Appl., 283 (1998) 289-299.

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