The Hadamard-type k-step Pell sequences
- 10 June 2022
- journal article
- research article
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 28 (2), 339-349
- https://doi.org/10.7546/nntdm.2022.28.2.339-349
Abstract
In this paper, we define the Hadamard-type k-step Pell sequence by using the Hadamard-type product of characteristic polynomials of the Pell sequence and the k-step Pell sequence. Also, we derive the generating matrices for these sequences, and then we obtain relationships between the Hadamard-type k-step Pell sequences and these generating matrices. Furthermore, we produce the Binet formula for the Hadamard-type k-step Pell numbers for the case that k is odd integers and k >= 3. Finally, we derive some properties of the Hadamard-type k-step Pell sequences such as the combinatorial representation, the generating function, and the exponential representation by using its generating matrix.Keywords
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