Consider a series of integers $a$ defined by:
$$\begin{cases} a_n & = c_n & \text{if $0 \le n \le 2$} \\ a_{2n} & = f(a_n, a_{n+1}) & \text{if $n > 1$} \quad \text{(even $n$)} \\ a_{2n+1} & = g(a_{n-1}, a_n) & \text{if $n \ge 1$} \quad \text{(odd $n$)} \end{cases}$$
where $c_0, c_1, c_2$ are constants. The subscript of the second and third cases is meant to convey multiplication (e.g. for $n=5,\enspace a_{10} = f(a_4, a_5)$).
It seems very similar to a recurrence relation, as latter terms are defined as a function of previous terms, except for the fact that the series isn't defined sequentially.
Note that for $a_6$ depends on terms $a_3$ and $a_4$ -- 3 and 2 terms "away", respectively -- while $a_{100}$ depends on terms $a_{50}$ and $a_{51}$.
Is this still a recurrence relation? If not (or if so, I suppose) is there a better name for this construction so I can get more information on how to approach generalizing it (i.e. calculating an arbitrary term without needing to generate the entire sequence).
Thanks in advance.
