Explicit a succession using z inverse transform Is it possible to explicit $y(n)$ of this mathematical succession in recursive form using z inverse transform?:

$ y(0) = 1 \\ y(n+1) = 2y(n) + 3 $

I can't write this as a linear system in z (linear difference equation) because there is the $3$ that doesn't depends on input or output.

I know some methods to solve this but I'm trying to use z inverse transform with no success.
If you are allowed to define your system to be causal so that it is non-zero only for $n \ge 0$, then you can use the unit step function $u[n]$ so that your system becomes:

$$y[0] = 1$$
$$y[n+1] = 2y[n] + 3u[n]$$

Which does have a Z-transform representation.