Products of Fermat or Mersenne numbers in some sequences

Let P-n be an n-th Padovan number, E-n an n-th Perrin number, and N-n an n-th Narayana number. In this paper, we solve the Diophantine equations P-n = (2(a) -1)(2(b) - 1), E-n = (2(a )-1)(2(b) - 1), and N-n = (2(a) +/- 1)(2(b) +/- 1), in positive integers n, a and b . Therefore, we determine the Padovan or Perrin numbers that are products of two Mersenne numbers and the Narayana numbers that are products of two Mersenne or Fermat numbers.