On One-Zero numbers: A new Horadam-type sequence

Authors

DOI:

https://doi.org/10.22481/intermaths.v5i2.15554

Keywords:

Horadam-type sequence, One-Zero sequence, Tagiuri-Vajda Identity, Partial sum

Abstract

In this paper, we present a new sequence of Horadam-type, which we call the One-Zero sequence. We study the recurrence equation and show the Binet formula. The aim of this study is to examine the properties of the aforementioned sequence. To this end, we have analyzed several classical identities, including the Tagiuri-Vajda and the Gelin-Cesàro identities. Additionally, we determine the partial sum of the terms of the One-Zero sequence.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

References

A. F. Horadam. “A generalized Fibonacci sequence.” The American Mathematical Monthly, v. 68, n. 5, p. 455–459, 1961.

A. F. Horadam. “Basic properties of a certain generalized sequence of numbers”, The Fi- bonacci Quart., v. 3, n. 3, p. 161–176, 1965.

D. Kalman; R. Mena. “The Fibonacci numbers-exposed”, Mathematics magazine, 76(3), 167–181, 2003.

N. J. A. Sloane. The on-line encyclopedia of integer sequences. Sequence A002275. [S. l.]: The OEIS Foundation Inc., 2024. Disponível em: http://oeis.org/A094028 .

C. A. Pickover. “Is There a Double Smoothly Undulating Integer?”. Journal of Recreational Mathematics, v.22, n.1, p. 52-53, 1990.

C. A. Pickover. Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. (Chapter 52 and 88). Oxford University Press, 2003.

E. A. Costa: G. A. Costa. “Existem nu ́meros primos na forma 101... 101”. Revista do Professor de Matemática, n. 103, p. 21-22, 2021.

F. S. Carvalho; E. A. Costa. “Um passeio pelos nu ́meros ondulantes”. REMAT: Revista Eletrônica da Matemática, Bento Gon ̧calves, v. 8, n. 2, p. e3001-e3001, 2022.

D. C. Santos; E. A. Costa. “Peculiarities of smoothly undulating number”. INTERMATHS, v. 4, n. 2, p. 38-53, 2023. https://doi.org/10.22481/intermaths.v4i2.13906

E. A. Costa; A. B. Souza. “Números ondulantes na forma 101...101”. Gazeta de Matemática, n. 202, p. 12-19, 2024. https://gazeta.spm.pt/fichaartigo?id=1682.

A. C. Morgado; P. C. P. Carvalho Matemática Discreta. SBM: Coleção ProfMat 16, Rio de Janeiro, 2015.

K. H. Rosen. Discrete mathematics and its applications. The McGraw Hill Companies, 2007.

D. C. Santos; E. A. Costa. “A note on Repunit number sequence”. Intermaths, 5(1), 54–66. 2024. https://doi.org/10.22481/intermaths.v5i1.14922.

D. C. Santos; E. A. Costa. “Um passeio pela sequência repunidade”. CQD-Revista Eletrônica Paulista de Matemática, p. 241-254, 2023.

E. A. Costa; D. C. Santos; F. S. Monteiro; V. M. A. Souza. “On the Repunit sequence at negative indices”. Revista de Matemática da UFOP, v. 1, p. 1-12, 2024. Disponível em <https://doi.org/10.5281/zenodo.11062161>.

Downloads

Published

2024-12-31

How to Cite

Costa, E. A., Costa, G. A., & Catarino, P. M. M. C. (2024). On One-Zero numbers: A new Horadam-type sequence. Intermaths, 5(2), 80-92. https://doi.org/10.22481/intermaths.v5i2.15554

Issue

Vol. 5 No. 2 (2024)

Section

Artigos

License

Copyright (c) 2024 Intermaths

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  • Responsibility: The scientific content and the opinions expressed in the manuscript are the sole responsibility of the author(s).
  • Copyrights: INTERMATHS. 
  • All content of Revista INTERMATHS/INTERMATHS journal is licensed under a Creative Commons - Atribuição 4.0 Internacional

Licença Creative Commons