The number N(h,s) of nonbranched cata-condensed benzenoids, including helicenes and other out-of-plane systems, is discussed in terms of two parameters: total number h of benzenoid rings, and number s of benzenoid rings in the longest linearly condensed portion. Recurrence formulas for N(h,s) are demonstrated by Theorems 1 and 2 and implemented by means of a computer program. For h ≤ 2s − 1, an explicit formula for N(h,s) is proved by Theorem 3; in this case, N(h,s) no longer depends separately on h and s, but only on the difference h − s.