A new direction of Fibonacci sequence modification

Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 12, 2006, Number 1, Pages 25–32
Full paper (PDF, 114 Kb)

Details

Authors and affiliations

Krassimir T. Atanassov
CLBME – Bulgarian Academy of Sciences
P.O.Box 12, Sofia-1113, Bulgaria

References

  1. Atanassov K., L. Atanassova, D. Sasselov, A new perspective to the generalization of the Fibonacci sequence, The Fibonacci Quarterly, Vol. 23 (1985), No. 1, 21-28.
  2. Atanassov K., On a second new generalization of the Fibonacci sequence. The Fibonacci Quarterly, Vol. 24 (1986), No. 4, 362-365.
  3. Lee J.-Z., J.-S. Lee, Some properties of the generalization of the Fibonacci sequence. The Fibonacci Quarterly, Vol. 25 (1987) No. 2, 111-117.
  4. Atanassov K., On a generalization of the Fibonacci sequence in the case of three sequences. The Fibonacci Quarterly, Vol. 27 (1989), No. 1, 7-10.
  5. Atanassov K., Remark on variants of Fibonacci squares. Bulletin of Number Theory and Related Topics, Vol. XIII (1989), 25-27.
  6. Atanassov K., A remark on a Fibonacci plane. Bulletin of Number Theory and Related Topics, Vol. XIII (1989), 69-71.
  7. Atanassov K., J. Hlebarova, S. Mihov, Recurrent formulas of the generalized Fibonacci and Tribonacci sequences, The Fibonacci Quarterly, Vol. 30 (1992), No. 1, 77-79.
  8. Spickerman W., R. Joyner, R. Creech, On the (2; F)-generalizations of the Fibonacci sequence, The Fibonacci Quarterly, Vol. 30 (1992), No. 4, 310-314.
  9. Shannon A., R. Melham, Carlitz generalizations of Lucas and Lehmer sequences, The Fibonacci Quarterly, Vol. 31 (1993), No. 2, 105-111.
  10. Spickerman W., R. Creech, R. Joyner, On the structure of the set of difference systems defining (3; F) generalized Fibonacci sequence, The Fibonacci Quarterly, Vol. 31 (1993), No. 4, 333-337.
  11. Spickerman W., R. Creech, R. Joyner, On the (3; F) generalizations of the Fibonacci sequence, The Fibonacci Quarterly, Vol. 33 (1995), No. 1, 9-12.
  12. Atanassov K., Remark on a new direction for a generalization of the Fibonacci sequence, The Fibonacci Quarterly, Vol. 33 (1995), No. 3, 249-250.
  13. Atanassov K., A. Shannon, J. Turner, The generation of trees from coupled third order recurrence relations, Research in Mathematics, Vol. 5, Blagoevgrad, 1995, 46-56.
  14. Randic M., D. Morales, O. Araujo, Higher-order Fibonacci numbers, Journal of Mathematical Chemistry, 1996, Vol.20, No.1-2, 79-94.
  15. Spickerman W., R. Creech, The (2; T) generalized Fibonacci sequences, The Fibonacci Quarterly, Vol. 35 (1997), No. 4, 358-360.
  16. Ando S., M. Hayashi, Counting the number of equivalence classes of (m; F) sequences and their generalizations, The Fibonacci Quarterly, Vol. 35 (1997), No. 1, 3-8.
  17. Dantchev S., A closed form of the (2; T)-generalizations of the Fibonacci sequence, The Fibonacci Quarterly, Vol. 36 (1998), No. 5, 448-451.
  18. Atanassov K., V. Atanassova, A. Shannon, J. Turner, New Visual Perspectives on Fi- bonacci Numbers. World Scientific, New Jersey, 2002.
  19. Atanassova V., A. Shannon, K. Atanassov, Sets of extensions of the Fibonacci sequences. Comptes Rendus de l’Academie bulgare des Sciences, Tome 56, 2003, No. 9, 9-12.
  20. Hirschhorn M., Non-trivial intertwined second-order recurrence relation. The Fibonacci Quarterly, Vol. 43 (2005), No. 4, 316-325.
  21. Hirschhorn, Coupled second-order recurrences. Fibonacci sequence, The Fibonacci Quarterly, Vol. 44 (2006), No. 1, 20-25.
  22. Hirschhorn, Coupled third-order recurrences. Fibonacci sequence, The Fibonacci Quarterly, Vol. 44 (2006), No. 1, 26-31.

Related papers

Cite this paper

Atanassov, K. T. (2006). A new direction of Fibonacci sequence modification. Notes on Number Theory and Discrete Mathematics, 12(1), 25-32.

Comments are closed.