Sequences And Series

Let the first term of a series be \(T_1=6\) and its \(r^{\text {th }}\) term \(T_r=3 T_{r-1}+6^r, r=2,3\),
............ \(n\). If the sum of the first \(n\) terms of this series is \(\frac{1}{5}\left(n^2-12 n+39\right)\left(4 \cdot 6^n-5 \cdot 3^n+1\right)\), then \(n\) is equal to ___________.