A new transfer-matrix algorithm for exact enumerations: Self-avoiding   polygons on the square lattice
  We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110. 
Nathan Clisby and Iwan Jensen
math-ph cond-mat.stat-mech math.CO math.MP