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The Hadamard-type k-step Pell sequences
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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.
Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)
Title: The Hadamard-type k-step Pell sequences
Description:
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.
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