Some higher-order identities for generalized bi-periodic Horadam sequences

Ho Hon Leung; Elif Tan

doi:10.3906/mat-1905-62

Some higher-order identities for generalized bi-periodic Horadam sequences

Ho Hon Leung, Elif Tan

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we derive higher-order identities for the generalized bi-periodic Horadam sequences. Some of our results generalize the identities for the classical Fibonacci sequences and Horadam sequences obtained by Hoggatt, Horadam and Waddill. As an application, we derive some congruence properties satisfied by the generalized bi-periodic Horadam sequences.

Original language	English
Pages (from-to)	1687-1700
Number of pages	14
Journal	Turkish Journal of Mathematics
Volume	44
Issue number	5
DOIs	https://doi.org/10.3906/mat-1905-62
Publication status	Published - 2020

Keywords

Congruence
Generalized fibonacci sequence
Generalized lucas sequence
Horadam sequence

ASJC Scopus subject areas

Mathematics(all)

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10.3906/mat-1905-62

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title = "Some higher-order identities for generalized bi-periodic Horadam sequences",

abstract = "In this paper, we derive higher-order identities for the generalized bi-periodic Horadam sequences. Some of our results generalize the identities for the classical Fibonacci sequences and Horadam sequences obtained by Hoggatt, Horadam and Waddill. As an application, we derive some congruence properties satisfied by the generalized bi-periodic Horadam sequences.",

keywords = "Congruence, Generalized fibonacci sequence, Generalized lucas sequence, Horadam sequence",

author = "Leung, {Ho Hon} and Elif Tan",

note = "Funding Information: We are grateful to the referee(s) for giving us helpful comments to improve the quality of this paper. We are grateful to Thotsaporn Thanatipanonda for his help in some algebraic computations by the computer program Maple. The second author is grateful to Dr. Mohamed Salim for the arrangement of her visit to United Arab Emirates University (UAEU) in February 2019. It is supported by UAEU UPAR Grant G00002599 (Fund No. 31S314). Publisher Copyright: {\textcopyright} T{\"U}BI˙TAK.",

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doi = "10.3906/mat-1905-62",

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T1 - Some higher-order identities for generalized bi-periodic Horadam sequences

AU - Leung, Ho Hon

AU - Tan, Elif

N1 - Funding Information: We are grateful to the referee(s) for giving us helpful comments to improve the quality of this paper. We are grateful to Thotsaporn Thanatipanonda for his help in some algebraic computations by the computer program Maple. The second author is grateful to Dr. Mohamed Salim for the arrangement of her visit to United Arab Emirates University (UAEU) in February 2019. It is supported by UAEU UPAR Grant G00002599 (Fund No. 31S314). Publisher Copyright: © TÜBI˙TAK.

PY - 2020

Y1 - 2020

N2 - In this paper, we derive higher-order identities for the generalized bi-periodic Horadam sequences. Some of our results generalize the identities for the classical Fibonacci sequences and Horadam sequences obtained by Hoggatt, Horadam and Waddill. As an application, we derive some congruence properties satisfied by the generalized bi-periodic Horadam sequences.

AB - In this paper, we derive higher-order identities for the generalized bi-periodic Horadam sequences. Some of our results generalize the identities for the classical Fibonacci sequences and Horadam sequences obtained by Hoggatt, Horadam and Waddill. As an application, we derive some congruence properties satisfied by the generalized bi-periodic Horadam sequences.

KW - Congruence

KW - Generalized fibonacci sequence

KW - Generalized lucas sequence

KW - Horadam sequence

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EP - 1700

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 5

ER -

Some higher-order identities for generalized bi-periodic Horadam sequences

Abstract

Keywords

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