I’m trying to solve this recurrence of a function of the height of a binary tree with a recursive tree.But I can’t find any pattern to solve it.

$n_l$ is the height of the left subtree, $n_r$ is the height of the right subtree and $n$ is the height of the tree.

$$

T(n) = begin{cases}

T(n_l)+T(n_r) + 1 & text{if } n ge 0,

\

1 & text{otherwise.}\

end{cases}

\ text{Given that }n_l+n_r+1=n

$$