Finding inverse z transform for two sided ROC? I have a z transform   $Y(z)=(z^2-z) /(z^2+1.3z+0.3)$

In this case i have two poles ,one at -0.3 and one at -1.0

I want to find inverse z transform of Y(z)

Following is my matlab code:

clc
clear all
close all
syms z n
num=[1 -1 0]
den=[1 1.3 0.3]
[r,p,k]=residuez(num,den)


We know that ztransform of δ(n) is 1 and ztransform of u[n] is 1/(1-z^-1)

Keeping value of r,p and k in mind,our partial fraction becomes:
$$Y(z)= \frac{2.86}{z-(-1)} -\frac{1.86}{z-(-0.3)}$$

keeping in view that ztransform of u[n] is 1/(1-z^-1)

$y[n]=2.86(-1)^nu(n) - 1.86(-0.3)^nu(n)$
This above line is inverse ztransform for ROC |z|>1

$y[n]=-2.86(-1)^nu(-n-1)+1.86(-0.3)^nu(-n-1)$

This above line is inverse ztransform for ROC |z|&lt;0.3

My question is that,how can i find inverse z transform for ROC  0.3&lt;|z|&lt;1

I have also attached a snapshot of a table of common z transform and i have higlighted two cases that i have used
Since you have two poles, you have to decompose $0.3 &lt;|z|&lt;1$ into two ROCs, $R_A$ and $R_B$ such that: $$R_A \cap R_B \subseteq \{0.3 &lt;|z| &lt; 1\}$$

Your poles are $z=-0.3$, $z=-1$, so you have two choices for each ROC:


$|z| &gt; 1$
$|z| &lt; 1$


and


$|z| &gt; 0.3$
$|z| &lt; 0.3$


The requested ROC is given by $R_A \cap R_B = \{|z| &lt; 1\}\cap\{|z| &gt; 0.3\} = \{0.3 &lt; |z| &lt; 1\}$

In this case (and using your table),

$$y[]=-2.86(−1)^{}[--1]−1.86(−0.3)^{}[]$$