A 2-coloring of $[1,n]$ can have $\frac{n^2}{2a(a^2+2a+3)} + O(n)$ monochromatic triples of the form $\{x,y,x+ay\}, a \geq 2$, but not less!

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+	On the number of monochromatic Schur triples	2003	Boris A. Datskovsky