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This provides the first nontrivial bound for a question posed by Jiang and Yepremyan.\n  More generally, for each $ \\ell \\ge 2$, we prove that there is a constant $c$ such that if an $n$-vertex graph is $\\varepsilon$-far from being triangle-free, with $\\varepsilon \\gg n^{-1/3\\ell}$, then it has at least $c \\, \\varepsilon^{3\\ell} n^{2\\ell+1}$ copies of $C_{2\\ell+1}$. 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