Common terms of k-Pell numbers and Padovan or Perrin numbers

Abstract

AbstractLet $$k\ge 2$$ k ≥ 2 . A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence, the first k terms are $$0,\ldots ,0,1$$ 0 , … , 0 , 1 and each term afterwards is given by the linear recurrence $$\begin{aligned} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}. \end{aligned}$$ P n ( k ) = 2 P n - 1 ( k ) + P n - 2 ( k ) + ⋯ + P n - k ( k ) . In this paper, we extend the previous work (Rihane and Togbé in Ann Math Inform 54:57–71, 2021) and investigate the Padovan and Perrin numbers in the k-Pell sequence.