A weak homomorphism from a graph G to a graph H is a mapping f from V(G) to V(H), where either f(x) = f(y) or {f(x), f(y)} is an element of E(H), and this holds for all {x, y} in E(G). A rectangular grid graph is formed by taking the Cartesian product of two paths. In this paper, we present a formula for calculating the number of weak homomorphisms from paths to rectangular grid graphs.
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