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

Resumo

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.