Factorizations and representations of the backward second-order linear recurrences

Journal of Computational and Applied Mathematics

Volumn 201, Issue 1, 2007, Pages 182-197

  Kilic, Emrah ^a   Tasci, Dursun ^a  

^a GAZI UNIVERSITY   (Turkey)

Author keywords

Determinant; Factorization; Permanent; Second order linear recurrences

Indexed keywords

MATRIX ALGEBRA; NUMBER THEORY; NUMERICAL METHODS; POLYNOMIALS; PROBLEM SOLVING;

CHEBYSHEV POLYNOMIALS; DETERMINANTS; FACTORIZATION; SECOND ORDER LINEAR RECURRENCES;

LINEAR SYSTEMS;

EID: 33846156280     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.02.012     Document Type: Article

References (30)

1. Bunder F.J. Zeckendorf representations using negative Fibonacci numbers. Fibonacci Quart. 30 2 (1992) 111-115
2. Byrd P.F. Problem B-12: a Lucas determinant. Fibonacci Quart. 1 4 (1963) 78
3. Cahill N.D., and Narayan D.A. Fibonacci and Lucas numbers as tridiagonal matrix determinants. Fibonacci Quart. 42 3 (2004) 216-221
4. Cahill N.D., D'Errica J.R., Narayan D.A., and Narayan J.Y. Fibonacci determinants. College Math. J. 3 3 (2002) 221-225
5. Cahill N., D'Ericco J.R., and Spence J.P. Complex factorizations of the Fibonacci and Lucas numbers. Fibonacci Quart. 41 1 (2003) 13-19
6. G. Golub, C. Van Loan, Matrix Computations, third ed., vol. 310, Johns Hopkins University Press, Baltimore, 1996, pp. 50-51.
7. Hoggatt Jr. V., and Long C. Divisibility properties of generalized Fibonacci polynomials. Fibonacci Quart. 12 2 (1974) 113-120
8. Horadam A.F. An alternative proof of a unique representation theorem. Fibonacci Quart. 32 5 (1994) 409-411
9. Horadam A.F. Unique minimal representation of integers by negatively subscripted Pell numbers. Fibonacci Quart. 32 3 (1994) 202-206
10. Horn R.A., and Johnson C.R. Matrix Analysis (1990), Cambridge University Press, Cambridge, New York
11. E. Kilic, Factorizations and representations of the second order linear recurrences, submitted for publication.
12. E. Kilic, D. Tasci, On families of Bipartite graphs associated with sums of Fibonacci and Lucas numbers, Ars Combin., to appear.
13. E. Kilic, D. Tasci, On the generalized order-k Fibonacci and Lucas numbers, Rocky Mountain J. Math., to appear.
14. E. Kilic, D. Tasci, On the permanents of some tridiagonal matrices with applications to the Fibonacci and Lucas numbers, Rocky Mountain J. Math., to appear.
15. E. Kilic, D. Tasci, On the second order linear recurrences by tridiagonal matrices, Ars Combin., to appear.
16. E. Kilic, D. Tasci, On the second order linear recurrence satisfied by the permanent of generalized doubly stochastic matrices, Ars Combin., to appear.
17. E. Kilic, D. Tasci, On the generalized Fibonacci and Pell sequences by Hessenberg matrices, Ars Combin., to appear.
18. Lehmer D. Fibonacci and related sequences in periodic tridiagonal matrices. Fibonacci Quart. 13 (1975) 150-158
19. Margado J. Note on the Chebyshev polynomials and applications to the Fibonacci numbers. Port. Math. 52 (1995) 363-378
20. Minc H. Permanents of (0, 1)-circulants. Canad. Math. Bull. 7 2 (1964) 253-263
21. Minc H. Permanents, Encyclopedia of Mathematics and its Applications (1978), Addison-Wesley, New York
22. Püschel M., and Moura J.M.F. The algebraic approach to the discrete cosine and sine transforms and their fast algorithms. SIAM J. Comput. 32 5 (2003) 1280-1316
23. Rivlin T. Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory. second ed. (1990), Wiley, New York
24. Robbins N. Beginning Number Theory, Dubuque (1993), Wm. C. Brown Publishers, Iowa
25. Strang G. Introduction to Linear Algebra. second ed. (1998), Wellesley-Cambridge, Wellesley MA
26. Strang G. The discrete cosine transform. SIAM Rev. 41 (1999) 135-147
27. Strang G., and Borre K. Linear Algebra, Geodesy and GPS (1997), Wellesley-Cambridge, Wellesley MA pp. 555-557
28. Tasci D., and Kilic E. On the order-k generalized Lucas numbers. Appl. Math. Comput. 155 3 (2004) 637-641
29. Webb W.A., and Parberry E.A. Divisibility properties of Fibonacci polynomials. Fibonacci Quart. 7 5 (1969) 457-463
30. Zhang F. Matrix Theory (1999), Springer, New York, Berlin, Heidelberg