Counting all self-avoiding walks on a finite lattice strip of width one and two

In this paper, a closed-form expression for counting all SAWs, irrespective of length, but restricted to the finite lattice strip (-a, . . ., 0, . . ., b) × (0, 1), shall be obtained in terms of the non-negative integer parameters a and b. In addition, the argument used to prove this result will be extended to establish an enumerating formula for counting all SAWs, irrespective of length, but restricted to the half-finite lattice strip of width two (0, 1, . . ., n) × (0, 1, 2), in terms of n.