Relations for generalized Fibonacci and Tribonacci sequences

Robert Frontczak
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 1, Pages 178—192
DOI: 10.7546/nntdm.2019.25.1.178-192
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Authors and affiliations

Robert Frontczak
Landesbank Baden-Württemberg
Am Hauptbahnhof 2, 70173 Stuttgart, Germany


In this article, we are concerned with connections between generalized Fibonacci and Tribonacci sequences. The identities we derive are of convolution type. As particular examples, we state several identities between Fibonacci and Tribonacci numbers, Fibonacci and Tribonacci–Lucas numbers, Lucas and Tribonacci numbers and Lucas and Tribonacci–Lucas numbers, respectively. Our results provide extensions of some recently obtained identities.


  • Generating function
  • Fibonacci number
  • Tribonacci number

2010 Mathematics Subject Classification

  • 11B37
  • 11B39


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Cite this paper

Frontczak, R. (2019). Relations for generalized Fibonacci and Tribonacci sequences. Notes on Number Theory and Discrete Mathematics, 25(1), 178-192, DOI: 10.7546/nntdm.2019.25.1.178-192.

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