Abstract
Using computer enumerations and a rational approximant method of series analysis, we conjecture an expression for the first perimeter moment of directed animals on the square lattice which are confined in a strip of a given width with open boundary conditions. When the width tends to infinity, the conjecture leads to an algebraic series for the first perimeter moment of directed animals on one-half of the square lattice, similar to Conway's earlier conjecture for the whole square lattice.
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