The amplitude of Motzkin paths

Helmut Prodinger
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 41—47
DOI: 10.7546/nntdm.2022.28.1.41-47
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Authors and affiliations

Helmut Prodinger
Department of Mathematics, University of Stellenbosch
Stellenbosch 7602, South Africa


The amplitude of Motzkin paths was recently introduced, which is basically twice the height. We analyze this parameter using generating functions.


  • Motzkin paths
  • Height
  • Amplitude
  • Generating functions
  • Asymptotics

2020 Mathematics Subject Classification

  • 05A15


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Manuscript history

  • Received: 21 April 2021
  • Revised: 16 December 2022
  • Accepted: 25 January 2022
  • Online First: 7 February 2022

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Cite this paper

Prodinger, H. (2022). The amplitude of Motzkin paths. Notes on Number Theory and Discrete Mathematics, 28(1), 41-47, DOI: 10.7546/nntdm.2022.28.1.41-47.

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