Scrambler generator polynomial with initial state A length-$127$ frame scramble uses the following generator polynomial

$$G(D)= D^7+D^4+1$$


If the all-ones initial state is used, how can one obtain the $127$ bit sequence? I am not interested in the sequence itself or computer algorithm but an understanding of how to obtain in.
My understanding is that $G(D)$ is the $\mathcal Z$-transform of the impulse response $\textrm{1001001}$. Is this convolved with the initial state $\textrm{1111111}$?
This generating (check if it's a primitive polynomial - those are usually used) polynomial representing a simple Linear Feedback Shift Register (LFSR). The circuit is given below, the gate is a XOR gate (an addition over GF(2) ). You can follow the output of this shift register very easily