How one can solve the following recurrence: \begin{align} X[i,0] &=0 \quad \forall i =1,\ldots, m\\ X[m,n] &= a_n X[m,n-1]+b_n \sum_{i=k_m}^{m-1}X[i,i] +c_n \end{align}

Where $a_i\ge 1 ,~ 0 \le c_i , b_i <1, k_i \ge 1$ are constants for all $i = 1,\ldots, n$.