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

Abstract

Abstract Let k ≥ 2. A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence, the first k terms are 0,..., 0, 1 and each term afterwards is given by the linear recurrence P(k) n = 2P(k) n−1 + P(k) n−2 +···+ P(k) n−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