There are only two cases possible for $n^{th}$ position –

Case $1$ :– Parked car is not a truck.

Two options are available for $n^{th}$ position ie sedan or SUV can be parked at $n^{th}$ position. Now for the remaining $(n-1)$ positions we can park in $T_{n-1}$ ways.

$\therefore$ Number of ways to park = $2 * T_{n-1}$.

Case $2$ :– Parked car is a truck.

Truck takes $n^{th}$ and $(n-1)^{th}$ position. Now as per given conditions we cannot park another truck at $(n-2)^{th}$ position. Like case $1$, two options are available for $(n-2)^{th}$ position ie sedan or SUV can be parked at $(n-2)^{th}$ position. Now for the remaining $(n-3)$ positions we can park in $T_{n-3}$ ways.

$\therefore$ Number of ways to park = $2 * T_{n-3}$.

Therefore, recurrence relation for $T_n$ is $2 * T_{n-1} + 2 * T_{n-3}$.