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

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 Pn(k)=2Pn-1(k)+Pn-2(k)+⋯+Pn-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.