Pseudoknot RNA Structures with Arc-Length $\ge 3$

In this paper we study k-noncrossing RNA structures with arc-length ≥ 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 S k,3 (n) denote their number. Based on a novel functional equation for the generating function P n≥0 S k,3 (n)z n , we derive for arbitrary k ≥ 3 exponential growth factors and for k = 3 the subexponential factor.