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The main goal of this note is to establish a connection between the fuzzy subgroups of a finite cyclic group with k direct factors and the lattice paths of Z k . This leads us to an explicit formula for the wellknown central Delannoy numbers.doi:10.1016/j.ejc.2007.12.005 fatcat:fdkvzqyimve4hgzpocvp6zn74q