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

Eudes Antonio Costa; Grieg Antonio Costa; Paula Maria Machado Cruz Catarino

doi:10.22481/intermaths.v5i2.15554

Authors

Eudes Antonio Costa https://orcid.org/0000-0001-6684-9961
Grieg Antonio Costa https://orcid.org/0009-0009-2611-8481
Paula Maria Machado Cruz Catarino https://orcid.org/0000-0001-6917-5093

DOI:

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

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.

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References

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