  We show that there is a measure-preserving system $(X,\mathscr{B}, \mu, T)$
together with functions $F_0, F_1, F_2 \in L^{\infty}(\mu)$ such that the
correlation sequence $C_{F_0, F_1, F_2}(n) = \int_X F_0 \cdot T^n F_1 \cdot
T^{2n} F_2 d\mu$ is not an approximate integral combination of $2$-step
nilsequences.
