Some properties of the bi-periodic Horadam sequences

Elif Tan
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 4, Pages 56—65
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Authors and affiliations

Elif Tan
Department of Bioinformatics and Mathematical Modelling
Department of Mathematics, Ankara University
Ankara, Turkey


In this paper, we give some basic properties of the bi-periodic Horadam sequences which generalize the known results for the bi-periodic Fibonacci and Lucas sequences. Also, we obtain some new identities for the bi-periodic Lucas sequences.


  • Horadam sequence
  • Conditional sequence
  • Bi-periodic Fibonacci sequence

AMS Classification

  • 11B39
  • 05A15


  1. Bilgici, G. (2014) Two generalizations of Lucas sequence. Appl. Math. Comput., 245, 526–538.
  2. Edson, M., Lewis, S. & Yayenie, O. (2011) The k-Periodic Fibonacci Sequence and an Extended Binet’s Formula, Integers, 11, 739–751.
  3. Edson, M. & Yayenie, O. (2009) A new generalizations of Fibonacci sequences and extended Binet’s Formula, Integers, 9, 639–654.
  4. Horadam, A. F. (1965) Basic Properties of a Certain Generalized Sequence of Numbers, Fibonacci Quart., 3(3), 161–176.
  5. Panario, D., Sahin, M. &Wang, Q. (2011) A family of Fibonacci-like conditional sequences, Integers, 13 (2013), (A78).
  6. Sahin, M. (2011) The Gelin–Cesaro identity in some conditional sequences, Hacet. J. Math. Stat., 40(6), 855–861.
  7. Tan, E. & Ekin, A. B. (2014) On convergence properties of Fibonacci-like conditional sequences. Commun. Fac. Sci. Univ. Ank. S´er. A1 Math. Stat., 63(2), 119–127.
  8. Tan, E. & Ekin, A. B. (2017) Some Identities On Conditional Sequences By Using Matrix Method. Miskolc Mathematical Notes, 18(1), 469–477.
  9. Tan, E. & Ekin, A. B. (2015) Bi-Periodic Incomplete Lucas Sequences. Ars Combinatoria, 123, 371–380.
  10. Yayenie, O. (2011) A note on generalized Fibonacci sequence, Appl. Math. Comput., 217, 5603–5611.

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Cite this paper

Tan, E. (2017). Some Properties of the Bi-periodic Horadam Sequences. Notes on Number Theory and Discrete Mathematics, 23(4), 56-65.

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