  The Tribonacci sequence is a well-known example of third order recurrence
sequence, which belongs to a particular class of recursive sequences. In this
article, other generalized Tribonacci sequence is introduced and defined by
$H_{n+2}=H_{n+1}+H_{n}+H_{n-1}\ \ (n\geq 1)$, where $H_{0}=3$, $H_{1}=0$ and
$H_{2}=2$. Also $n$-th power of the generating matrix for this generalized
Tribonacci sequence is established and some basic properties of this sequence
are obtained by matrix methods. There are many elementary formulae relating the
various $H_{n}$, most of which, since the sequence is defined inductively, are
themselves usually proved by induction.
