Suppose an algorithm has a runtime recurrence relation:$   T(n) = \left\{     \begin{array}{lr}       g(n)+T(n-1) + T(\lfloor\delta n\rfloor ) & : n \ge n_0\\       f(n) & : n < n_0     \end{array}   \right.$  for some constant $0 < \delta < 1$. Assume that $g$ is polynomial in $n$, perhaps quadratic. Most likely, $f$ will be exponential in $n$.How would one go about analyzing the runtime ($\Theta$ would be excellent)? The master theorem and the more general Akra-Bazzi method do not seem to apply.
Asymptotic approximation of a recurrence relation (Akra-Bazzi doesn't seem to apply)
asymptotics;recurrence relation