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

Abstract

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.

Keywords

  • Generating function
  • Fibonacci number
  • Tribonacci number

2010 Mathematics Subject Classification

  • 11B37
  • 11B39

References

  1. Adegoke, K. (2018). Squares of Tribonacci numbers, Preprint, Available online: https: //arxiv.org/abs/1805.07855v2.
  2. Adegoke, K. (2018). Weighted sums of some second-order sequences, Fibonacci Quart., 56 (3), 252–262.
  3. Cook, C. K.., & Komatsu, T. (2016). Some identities for sequences of binomial sums of generalized Fibonacci numbers, Fibonacci Quart., 54 (2), 105–111.
  4. Frontczak, R. (2018). Convolutions for generalized Tribonacci numbers and related results, Int. J. Math. Anal., 12 (7), 307–324.
  5. Frontczak, R. (2018). Some Fibonacci–Lucas–Tribonacci–Lucas identities, Fibonacci Quart., 56 (3), 263–274.
  6. Mezö, I. (2009). Several generating functions for second-order recurrence sequences, J. Integer Seq., 12, Article 09.3.7.
  7. Tanackov, I. (2018). Binet type formula for Tribonacci sequence with arbitrary initial numbers, Chaos Solitons Fractals, 114, 63–68.
  8. Sloane, N. J. A. The On-Line Encyclopedia of Integer Sequences, Published electronically: https://oeis.org.

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Cite this paper

APA

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.

Chicago

Frontczak, Robert. “Relations for Generalized Fibonacci and Tribonacci Sequences.” Notes on Number Theory and Discrete Mathematics 25, no. 1 (2019): 178-192, doi: 10.7546/nntdm.2019.25.1.178-192.

MLA

Frontczak, Robert. “Relations for Generalized Fibonacci and Tribonacci Sequences.” Notes on Number Theory and Discrete Mathematics 25.1 (2019): 178-192. Print, doi: 10.7546/nntdm.2019.25.1.178-192.

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