By extending the method of the author’s earlier paper, a purely recursive approach is devised for counting the total number of unfolded self-avoiding walks terminating along the line , within the finite lattice strip of width three. This approach yields a generating function for the sequence of numbers just described, without the need for any exact enumeration, usually entailed with an application of the transfer matrix algorithm. As a result of determining this generating function, the total number of unfolded walks within the lattice strip can then be easily computed.
"Counting all unfolded self-avoiding walks on a finite lattice strip of width three." Rocky Mountain J. Math. 50 (6) 2179 - 2197, December 2020. https://doi.org/10.1216/rmj.2020.50.2179