设数列\(\{a _{n} \}\)满足\(a _{1} =2\)，\(a _{2} =6\)，\(a _{3} =12\)，数列\(\{a _{n} \}\)前\(n\)项和为\(S _{n}\)，且\( \dfrac {S_{n+2}-S_{n-1}+1}{S_{n+1}-S_{n}+1}=3 (n∈N*\)且\(n\geqslant 2).\)若\([x]\)表示不超过\(x\)的最大整数，\(b_{n}=[ \dfrac {(n+1)^{2}}{a_{n}}]\)，数列\(\{b _{n} \}\)的前\(n\)项和为\(T _{n}\)，则\(T _{2020} = (\:\:\:\:)\)