Recursive formulas are derived for generating the conjugatedcircuit polynomials for circuits up to size n = 6, 10, or 14 on regular chain polyhex graphs. These counting polynomials are of use for a simple valencebond resonancetheoretic derived model: the conjugatedcircuit model. 1994 John Wiley & Sons, Inc. Copyright 1994 John Wiley & Sons, Inc.