  In this paper we study $k$-noncrossing RNA structures with arc-length $\ge
3$, i.e. RNA molecules in which for any $i$, the nucleotides labeled $i$ and
$i+j$ ($j=1,2$) cannot form a bond and in which there are at most $k-1$
mutually crossing arcs. Let ${\sf S}_{k,3}(n)$ denote their number. Based on a
novel functional equation for the generating function $\sum_{n\ge 0}{\sf
S}_{k,3}(n)z^n$, we derive for arbitrary $k\ge 3$ exponential growth factors
and for $k=3$ the subexponential factor. Our main result is the derivation of
the formula ${\sf S}_{3,3}(n) \sim \frac{6.11170\cdot 4!}{n(n-1)...(n-4)}
4.54920^n$.
