Is there a general way of evaluating the points in a recurrence relation when the initial conditions are not contiguous? For instance:
$$T(i) = f\left(T(i-1), T(i-2)\right),$$ with $T(a) = A$ and $T(b) = B$, and $a+1 \leq i \leq b-1$ (and with whatever $f$ and $a < b+1$).
I am concerned with the (possibly numeric) evaluation of $T(i)$, not with the solution of the above equation (since it has no closed-form solution in the general case).
If it is not possible in general, what about particular cases (other than $b$ = $a+1$ or $f$ "solvable").