On the $X$-coordinates of Pell equations which are Tribonacci numbers
  For an integer $d\geq 2$ which is not a square, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=\pm 1$ which is a Tribonacci number, with a few exceptions that we completely characterize. 
Florian Luca, Amanda Montejano, Laszlo Szalay and Alain Togb\'e
math.NT