On a quaternionic sequence with Vietoris' numbers

Abstract

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.