We consider sequences that encode boundary circuits of fused polycycles made up of polygonal faces withp sides, p ≤ 6. We give a constructive algorithm for recognizing such sequences when p = 5 or 6. Asimpler algorithm is given for planar hexagonal sequences. Hexagonal and pentagonal sequences of lengthat most 8 are tabulated, the former corresponding to planar benzenoid hydrocarbons CxHy with y up to 14.