The first study of resonances in $^{17}$O+$alpha$ elastic scattering was carried out using the Thick Target Inverse Kinematics (TTIK) method. The data were analyzed in the framework of an $textit{R}$-matrix approach. Many $alpha$-cluster states were found in the $^{21}$Ne excitation region of the 9-13 MeV excitation energy including the first observation of a broad $textit{l}$=0 state in an odd-even nucleus, which is likely the analog of the broad 0$^+$ at 8 MeV in $^{20}$Ne. The observed structure in $^{21}$Ne appeared to be strikingly similar to that in $^{20}$Ne populated in the resonance $^{16}$O+$alpha$ scattering. The results are also useful for refinement of data on an $^{17}$O($alpha$,$textit{n}$) reaction important for astrophysics.
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