How to change the variables so $x_{n+3}=f(x_{n},x_{n+1},x_{n+2})$ becomes of the form $g(y_n)=y_{n+1}$?

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How to change the variables so $x_{n+3}=f(x_{n},x_{n+1},x_{n+2})$ becomes of the form $g(\underline{y}_n)=\underline{y}_{n+1}$

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$\underline{y_{n+1}}=g(\underline{y_n})=g(x_n,x_{n+1},x_{n+2})=(x_{n+1},x_{n+2},f(x_n,x_{n+1},x_{n+2}))$