Generalized Euler–Seidel method for second order recurrence relations

M. Cetin Firengiz and A. Dil
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 4, Pages 21—32
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Authors and affiliations

M. Cetin Firengiz
Department of Mathematics Education, Başkent University
Baglıca 06810 Ankara, Turkey
* Corresponding author

A. Dil
Department of Mathematics, Akdeniz University
07058 Antalya, Turkey


We obtain identities for the generalized second order recurrence relation by using the generalized Euler–Seidel matrix with parameters x, y. As a consequence, we give some properties and generating functions of well-known special integer sequences.


  • Generalized Euler–Seidel matrix
  • Fibonacci sequence
  • Lucas sequence
  • Pell sequence
  • Jacobsthal sequence
  • Generating function

AMS Classification

  • 11B39
  • 11B83


  1. Chen, K.-W., Identities From the Binomial Transform, J. Number Theory, Vol. 124, 2007, No. 1, 142–150.
  2. Dumont, D., Matrices d’Euler–Seidel, Seminaire Lotharingien de Combinatorie, 1981,B05c.
  3. Dil, A., I. Mező, Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers, Appl. Math. Comput., Vol. 206, 2008, 942–951.
  4. Euler, L., De Transformatione Serierum, Opera Omnia, series prima, Vol. X, Teubner, 1913.
  5. Horadam, A. F., Basic Properties of a Certain Generalized Sequence of Numbers, Fibonacci Quart., Vol. 3, 1965, No. 3, 161-176.
  6. Horadam, A. F., Pell Identities, Fibonacci Quart., Vol. 9, 1971, No. 3, 245–263.
  7. Mező, I., A. Dil, Euler–Seidel Method for Certain Combinatorial Numbers and A New Characterization of Fibonacci Sequence, Cent. Eur. J. Math., Vol. 7, 2009, No. 2, 310–321.
  8. Mező, I., Several Generating Functions for Second-Order Recurrence Sequences, J. Integer Seq. Vol. 12, 2009, Article 09.3.7.
  9. Seidel, L., Über Eine Einfache Enstehung Weise der Bernoullischen Zahlen und Einiger Verwandten Reihen, Sitzungsberichte der Münch. Akad. Math. Phys. Classe, 1877, 157–187.

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Cite this paper

Cetin Firengiz, M, & Dil, A. (2014). Generalized Euler–Seidel method for second order recurrence relations. Notes on Number Theory and Discrete Mathematics, 20(4), 21-32.

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