# Expression for an intersection of two series

I have two series, one of the form $$S_1=u(u+1)$$ and another of the form $$S_2=u(13u\pm 1)$$, which leads to $$S_1=2,6,12,20,...$$ and $$S_2= ...,114,50,12,0,14,54,120,...$$. Then a third series is formed given by $$S_3=S_1 \cap S_2$$, meaning $$S_3=12,462,54990,...$$. I would like to know if $$S_3$$ can be expressed in terms of $$u$$?