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  • Research Article
  • Open Access

Extending generalized Fibonacci sequences and their binet-type formula

Advances in Difference Equations20062006:023849

  • Received: 8 May 2006
  • Accepted: 2 July 2006
  • Published:


We study the extension problem of a given sequence defined by a finite order recurrence to a sequence defined by an infinite order recurrence with periodic coefficient sequence. We also study infinite order recurrence relations in a strong sense and give a complete answer to the extension problem. We also obtain a Binet-type formula, answering several open questions about these sequences and their characteristic power series.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation


Authors’ Affiliations

Section de Mathématique, LEGT - F. Arago, Académie de Reims, 1, rue F. Arago, Reims, 51100, France
Faculty of Mathematics, Kyushu University, Hakozaki Fukuoka, 812-8581, Japan


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© M. Rachidi and O. Saeki 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.