Special integers sequences have been the center of attention for many researchers, as well as the sequences of quaternions where its components are the elements of these sequences. Motivated by a rational sequence, we consider the quaternions with components Vietoris' numbers and investigate some of its properties. For this sequence a two and three term recurrence relation is established, as well as a Binet's type formula. Moreover the generating function for this sequence is introduced and also the determinant of some tridiagonal matrices are used in order to find elements of this sequence