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.
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