Research Article

A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients

Volume: 8 Number: 3 September 23, 2025
Elen Viviani Pereira Spreafico *, Eudes Antonio Costa , Paula Maria Machado Cruz Catarino
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Communications in Advanced Mathematical Sciences Cover Communications in Advanced Mathematical Sciences

A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients

Abstract

In this study, we define a new generalization of the hybrid $k$-Pell sequence consisting of hybrid numbers with generalized hybrid $k$-Pell numbers as coefficients. We establish some algebraic properties and also the Binet formula, generating function, and exponential generating function related to this new sequence. In addition, some identities are provided as sum identities, and Catalan, Cassini, and d'Ocagne's identities. The particular cases are studied, namely, the hybrid numbers with hybrid $k$-Pell numbers as coefficients, the hybrid numbers with hybrid $k$-Pell--Lucas numbers as coefficients, and the hybrid numbers with hybrid Modified $k$-Pell numbers as coefficients.

Keywords

Binet , Generating function , Hybrid numbers , Hybrid $k$-Pell sequence , Identities

References

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Early Pub Date

July 18, 2025

Publication Date

September 23, 2025

Submission Date

March 11, 2025

Acceptance Date

April 20, 2025

Published in Issue

Year 2025 Volume: 8 Number: 3

DOI

https://doi.org/10.33434/cams.1655752

IZ

https://izlik.org/JA49NM69HX

Cite

RIS / Bibtex
APA
Pereira Spreafico, E. V., Costa, E. A., & Catarino, P. M. M. C. (2025). A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients. Communications in Advanced Mathematical Sciences, 8(3), 125-135. https://doi.org/10.33434/cams.1655752
AMA
1.Pereira Spreafico EV, Costa EA, Catarino PMMC. A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients. Communications in Advanced Mathematical Sciences. 2025;8(3):125-135. doi:10.33434/cams.1655752
Chicago
Pereira Spreafico, Elen Viviani, Eudes Antonio Costa, and Paula Maria Machado Cruz Catarino. 2025. “A Note on Hybrid Numbers With Generalized Hybrid K-Pell Numbers As Coefficients”. Communications in Advanced Mathematical Sciences 8 (3): 125-35. https://doi.org/10.33434/cams.1655752.
EndNote
Pereira Spreafico EV, Costa EA, Catarino PMMC (September 1, 2025) A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients. Communications in Advanced Mathematical Sciences 8 3 125–135.
IEEE
[1]E. V. Pereira Spreafico, E. A. Costa, and P. M. M. C. Catarino, “A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients”, Communications in Advanced Mathematical Sciences, vol. 8, no. 3, pp. 125–135, Sept. 2025, doi: 10.33434/cams.1655752.
ISNAD
Pereira Spreafico, Elen Viviani - Costa, Eudes Antonio - Catarino, Paula Maria Machado Cruz. “A Note on Hybrid Numbers With Generalized Hybrid K-Pell Numbers As Coefficients”. Communications in Advanced Mathematical Sciences 8/3 (September 1, 2025): 125-135. https://doi.org/10.33434/cams.1655752.
JAMA
1.Pereira Spreafico EV, Costa EA, Catarino PMMC. A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients. Communications in Advanced Mathematical Sciences. 2025;8:125–135.
MLA
Pereira Spreafico, Elen Viviani, et al. “A Note on Hybrid Numbers With Generalized Hybrid K-Pell Numbers As Coefficients”. Communications in Advanced Mathematical Sciences, vol. 8, no. 3, Sept. 2025, pp. 125-3, doi:10.33434/cams.1655752.
Vancouver
1.Elen Viviani Pereira Spreafico, Eudes Antonio Costa, Paula Maria Machado Cruz Catarino. A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients. Communications in Advanced Mathematical Sciences. 2025 Sep. 1;8(3):125-3. doi:10.33434/cams.1655752

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