Common terms of \(k\)-Pell numbers and Padovan or Perrin numbers.(English)Zbl 1523.11035
Summary: Let \(k\ge 2\). A generalization of the well-known Pell sequence is the \(k\)-Pell sequence. For this sequence, the first \(k\) terms are \(0,\ldots ,0,1\) and each term afterwards is given by the linear recurrence\[P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}.\]In this paper, we extend the previous work [the last two authors, Ann. Math. Inform. 54, 57–71 (2021;Zbl 1499.11078)] and investigate the Padovan and Perrin numbers in the \(k\)-Pell sequence.
MSC:
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
| 11J86 | Linear forms in logarithms; Baker’s method |
Citations:
Zbl 1499.11078Software:
OEISCite
References:
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