The adjacency-Pell-Hurwitz numbers. (English) Zbl 1444.11049
Summary: In this paper, we define the \(k\)-adjacency-Pell-Hurwitz numbers by using the Hurwitz matrix of order \(4m\) which is obtained by the aid of the characteristic polynomial of the adjacency-Pell sequence. Firstly, we give relationships between the \(k\)-adjacencyPell-Hurwitz numbers and the generating matrices for these sequences. Further, we obtain the Binet formula for the \((2m-1)\)-adjacency-Pell-Hurwitz numbers. Also, we derive relationships between the \(k\)-adjacency-Pell-Hurwitz numbers and permanents and determinants of certain matrices. Finally, we give the combinatorial and exponential representations of the \(k\)-adjacency-Pell-Hurwitz numbers.
MSC:
| 11D09 | Quadratic and bilinear Diophantine equations |
Keywords:
adjacency-Pell-Hurwitz numbersReferences:
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