  Let $V_{n}$ denote the third order linear recursive sequence defined by the
initial values $V_{0}$, $V_{1}$ and $V_{2}$ and the recursion
$V_{n}=rV_{n-1}+sV_{n-2}+tV_{n-3}$ if $n\geq 3$, where $r$, $s$, and $t$ are
real constants. The $\{V_{n}\}_{n\geq0}$ are generalized Tribonacci numbers and
reduce to the usual Tribonacci numbers when $r=s=t=1$ and to the $3$-bonacci
numbers when $r=s=1$ and $t=0$. In this study, we introduced a quaternion
sequence which has not been introduced before. We show that the new quaternion
sequence that we introduced includes the previously introduced Tribonacci,
Padovan, Narayana and Third order Jacobsthal quaternion sequences. We obtained
the Binet formula, summation formula and the norm value for this new quaternion
sequence.
