W.Y.C. Chen and J.D. Louck,
The combinatorial power of the companion matrix,
Linear Algebra Appl. 232 (1996) 261-278.

Cited by


  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. G. Cerda-Morales, Identities for third order Jacobsthal quaternions, Adv. Appl. Clifford Algebras 27 (2017) 1043-1053.

  3. G. Cerda-Morales, The third order Jacobsthal octonions: Some combinatorial properties, arXiv:1710.00602.

  4. G. Cerda-Morales, A note on dual third order Jacobsthal vectors, arXiv:1712.08950.

  5. G. Cerda-Morales, Third-order Jacobsthal generalized quaternions, arXiv:1810.03152.

  6. S.-E. Cheng, Generating function proofs of identities and congruences, Ph.D. Thesis, Michigan State University, 2003.

  7. G.S. Cheon and H. Kim, A new aspect of Hankel matrices via Krylov matrix, Linear Algebra Appl. 438 (2013) 361-373.

  8. W.S. Chou, L.C. Hsu and P.J.S. Shiue, Application of Faà di Bruno's formula in characterization of inverse relations, J. Comput. Appl. Math. 190 (2006) 151-169.

  9. Z. Cinkir, A fast elementary algorithm for computing the determinant of Toeplitz matrices, J. Comput. Appl. Math. 255 (2014) 353-361.

  10. A. Daçdemir, The representation, generalized Binet formula and sums of the generalized Jacobsthal p-sequence, Hittite Journal of Science and Engineering 3 (2016) 99-104.

  11. Ö. Deveci and E. Karaduman, On the Padovan p-numbers, Hacettepe Journal of Mathematics and Statistics 46 (2017) 579-592.

  12. Ö. Deveci and A.G. Shannon, On the adjacency-type sequences, International Journal of Advances in Mathematics 2017 (2017) 10-24.

  13. B.-S. Du, S.-S. Huang and M.-C. Li, Generalized Fermat, double Fermat and Newton sequences, J. Number Theory 98 (2003) 172-183.

  14. T. Grubman, Y.A. Şekercioglu and D.R. Wood, Partitioning de Bruijn graphs into fixed-length cycles for robot identification and tracking, Discrete Appl. Math. 213 (2016) 101-113.

  15. I. Gültekin and Ö. Deveci, On the arrowhead-Fibonacci numbers, Open Math. 14 (2016) 1104-1113.

  16. T.-X. He, J.H.-C. Liao and P.J.-S. Shiue, Matrix representation of recursive sequences of order 3 and its applications, Journal of Mathematical Research with Applications 38 (2018) 221-235.

  17. T.-X He and P.J.-S. Shiue, On sequences of numbers and polynomials defined by linear recurrence relations of order 2, Int. J. Math. Math. Sci. 2009 (2009) Art. ID 709386, 21 pp.

  18. T.-X. He and P.J.-S. Shiue and T.-W. Weng, Sequences of numbers meet the generalized Gegenbauer-Humbert polynomials, ISRN Discrete Math. 2011 (2011) Art. ID 674167, 16 pp.

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

  20. N. Irmak and M. Alp, Tribonacci numbers with indices in arithmetic progression and their sums, Miskolc Math. Notes 14 (2013) 125-133.

  21. Y.E. Khatabi, Racines p-ièmes d'une matrice inversible et suites de Fibonacci, Ph.D. Thesis, Université Moulay Ismaïl, 2016.

  22. E. Kiliç, The generalized order-k Fibonacci–Pell sequence by matrix methods, J. Comput. Appl. Math. 209 (2007) 133-145.

  23. E. Kiliç, The Binet formula, sums and representations of generalized Fibonacci p-numbers, European J. Combin. 29 (2008) 701-711.

  24. E. Kiliç, Tribonacci sequences with certain indices and their sums, Ars Combin. 86 (2008) 13-22.

  25. E. Kiliç, Sums of the squares of terms of sequence {un}, Proc. Math. Sci. 118 (2008) 27-41.

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

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

  28. E. Kiliç, N. Ömür and Y.T. Ulutaş, Matrix representations for the second order recurrence , Ars Combin. 93 (2009) 181-190.

  29. E. Kiliç and P. Stanica, Generating matrices for weighted sums of second order linear recurrences, J. Integer Seq. 12 (2009) Article 09.2.7, 11 pp.

  30. E. Kiliç and D. Taşci, The generalized Binet formula, representation and sums of the generalized order-k Pell numbers, Taiwanese J. Math. 10 (2006) 1661-1670.

  31. 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.

  32. 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.

  33. A. Lim and J. Dai, On product of companion matrices, Linear Algebra Appl. 435 (2011) 2921-2935.

  34. Y. Liu and Q. Zhang, Dynamic mode decomposition of separated flow over a finite blunt plate: time-resolved particle image velocimetry measurements, Exp. Fluids 56 (2015) 1-17.

  35. T. MacHenry and K. Wong, A representation of multiplicative arithmetic functions by symmetric polynomials, arXiv:0711.3620.

  36. T. MacHenry and K. Wong, Degree k linear recursions mod (p), Rocky Mountain J. Math. 41 (2011) 1303-1327.

  37. T. Machenry and K. Wong, A correspondence between isobaric rings and multiplicative arithmetic functions, Rocky Mountain J. Math. 42 (2012) 1247ĘC1290.

  38. R.K. Mallik, Solutions of linear difference equations with variable coefficients, J. Math. Anal. Appl. 22(1998) 79-91.

  39. R.K. Mallik, On the solution of a third order linear homogeneous difference equation with variable coefficents, J. Difference Equ. Appl. 4 (1998) 501-521.

  40. R.K. Mallik, On the solution of a linear homogeneous difference equation with variable coefficients, SIAM J. Math. Anal. 31 (1999/00) 375-385.

  41. J.A. Marrero and M. Rachidi, Application of the companion factorization to linear non-autonomous area-preserving maps, Linear Multilinear Algebra, 60 (2012) 201-217.

  42. E. Özkan, Truncated Lucas sequence and its period, Appl. Math. Comput. 232 (2014) 285-291.

  43. J.L. Ramírez and V.F. Sirvent, A note on the k-Narayana sequence, Ann. Math. Inform. 45 (2015) 91-105.

  44. V. Rovenski and P. Walczak, Extrinsic geometric flows on foliated manifolds, I, arXiv:1003.1607.

  45. V. Rovenski and P. Walczak, Topics in Extrinsic Geometry of Codimension-one Foliations, Springer, 2011.

  46. 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.

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

  48. A. Yalciner, On generalizations of two curious divisibility properties, Miskolc Math. Notes 14 (2013) 1085-1089.

  49. S.L. Yang, On the k-generalized Lucas numbers, International Journal of Pure and Applied Mathematics 21 (2005) 293-297.

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

  51. Q.S. Zhang, Y.Z. Liu and S.F. Wang, The identification of coherent structures using proper orthogonal decomposition and dynamic mode decomposition, Journal of Fluids and Structures 49 (2014) 53-72.

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