Answer
$a_1=1$
$a_2=2$
$a_3=3$
$a_n=a_{n-3}+a_{n-2}-a_{n-1}$ for $n>3$
Work Step by Step
For example, consider the sequence:
$$\begin{cases}
a_1=1\\
a_2=2\\
a_3=3\\
a_n=a_{n-3}+a_{n-2}-a_{n-1}\text{ for }n>3.
\end{cases}$$
Calculate the first eight terms of the sequence:
$$\begin{align*}
a_1&=1\\
a_2&=2\\
a_3&=3\\
a_4&=1+2-3=0\\
a_5&=2+3-0=5\\
a_6&=3+0-5=-2\\
a_7&=0+5-(-2)=7\\
a_8&=5+(-2)-7=-4.
\end{align*}$$
