TY  - JOUR
T1  - A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients
AU  - Pereira Spreafico, Elen Viviani
AU  - Costa, Eudes Antonio
AU  - Catarino, Paula Maria Machado Cruz
PY  - 2025
DA  - September
Y2  - 2025
DO  - 10.33434/cams.1655752
JF  - Communications in Advanced Mathematical Sciences
PB  - Emrah Evren KARA
WT  - DergiPark
SN  - 2651-4001
SP  - 125
EP  - 135
VL  - 8
IS  - 3
LA  - en
AB  - 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.
KW  - Binet
KW  - Generating function
KW  - Hybrid numbers
KW  - Hybrid $k$-Pell sequence
KW  - Identities
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UR  - https://doi.org/10.33434/cams.1655752
L1  - https://dergipark.org.tr/en/download/article-file/4681539
ER  -