The structure and thermodynamic parameters of [HMYH]_n (M = B, Al, Ga, In; Y = N, P, As; n = 10, 13, 16) oligomers are calculated by the B3LYP/LANL2DZ(d, p) method. For any MY pair, the rodlike structure is more stable than the fullerene-like structure and its stability increases with increasing n. The isolated squares rule is inapplicable to these systems and cannot serve as a basis for search for the most stable oligomers. The formation of [HMYH]_n oligomers from hydrides in the gas phase is thermodynamically favorable even at high temperatures (1000 K). The existence of rodlike inorganic polymers with a backbone consisting of fused M ₃Y₃ rings is predicted.