Use recursion tree to solve the recurrence

$T(n)=3T(n-3)+1$

The number of branches coming out of each internal node is:

The value in the first$-$level $($root$)$ node is:

The number of nodes on the second level is:

The sum of the values in the second$-$level nodes is:

The number of nodes on the third level is:

The sum of the values in the third$-$level nodes is:

The height of the tree is $($including the base if it is a logarithm$)$:

The sum of the values in the whole tree is in: Theta$($