Fibonacci numbers along residue classes and convolutions

Helmut Prodinger
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 2, Pages 374–377
DOI: 10.7546/nntdm.2026.32.2.374-377
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Authors and affiliations

Helmut Prodinger

1 Department of Mathematics, University of Stellenbosch
7602, Stellenbosch, South Africa
2 NITheCS (National Institute for Theoretical and Computational Sciences)
South Africa

Abstract

The sequence F_{dn+h} and its convolutions have (for h=0) been studied in a recent paper [3]. The instance with general h is more involved and uses Chebyshev polynomials.

Keywords

  • d-sections of Fibonacci numbers
  • Convolutions
  • Chebyshev polynomials
  • Generating functions

2020 Mathematics Subject Classification

  • 11B39

References

  1. Andrews, G. E., Askey, R., & Roy, R. (1999). Special Functions. Cambridge University Press.
  2. Horadam, A. F. (1969). Tschebyscheff and other functions associated with the sequence w_n\{a, b; p, q\}. The Fibonacci Quarterly, 7(1), 14–22.
  3. Khamitov, V. M., Dmitrishin, D. V., Stokolos, A. M., & Gray, D. A. (2026). Convolved numbers of k-section of the Fibonacci sequence: Properties, consequences. Herald of Advanced of Information Technology, 9(2), 129–139.

Manuscript history

  • Received: 9 May 2026
  • Revised: 19 August 2026
  • Accepted: 20 August 2026
  • Online First: 20 August 2026

Copyright information

Ⓒ 2026 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Prodinger, H. (2026). Fibonacci numbers along residue classes and convolutions. Notes on Number Theory and Discrete Mathematics, 32(2), 374-377, DOI: 10.7546/nntdm.2026.32.2.374-377.

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