  In this paper we derive the generating function of RNA structures with
pseudoknots. We enumerate all $k$-noncrossing RNA pseudoknot structures
categorized by their maximal sets of mutually intersecting arcs. In addition we
enumerate pseudoknot structures over circular RNA. For 3-noncrossing RNA
structures and RNA secondary structures we present a novel 4-term recursion
formula and a 2-term recursion, respectively. Furthermore we enumerate for
arbitrary $k$ all $k$-noncrossing, restricted RNA structures i.e.
$k$-noncrossing RNA structures without 2-arcs i.e. arcs of the form $(i,i+2)$,
for $1\le i\le n-2$.
