$f(x)=(1+x+x^2)^{2020}$
$=\sum\limits_{k=0}^{2020}C_{2020}^k.(x^2+x)^k$
$=\sum\limits_{k=0}^{2020}C_{2020}^k.\Big( \sum\limits_{i=0}^k.C_k^i.x^{2k-2i}x^i\Big)$
Tổng $S$ là tổng hệ số
$\to S=\sum\limits_{k=0}^{2020}C_{2020}^k.\sum\limits_{i=0}^k.C_k^i$
Nhận thấy khi $x=1$: $f(1)=S$ (do $1^n=1\forall n$)
$\to S=f(1)=3^{2020}$