In this paper, we study the class of Zp-double cyclic codes of length n = r + s. We give a closed formula for the number of Zp-double cyclic codes of length n = r + s, for any integers r and s that are relatively prime to p. Moreover, we give a closed formula for the number of quasi-cyclic (QC) codes of length n = 2s and index 2. We also provide formulas for the number of separable and non-separable Zp-double cyclic codes of length n. In order to illustrate the results, we calculate the number of some codes with different r and s. Moreover, we list optimal parameter Z2-double cyclic codes for specific values of r and s.

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