```python
import numpy as np
import sympy as sy
from sympy import init_printing
init_printing()
import control.matlab as cm
```

# The Fibonacci sequence

\begin{equation}
y(k+2) - y(k+1) - y(k) = 0
\end{equation}




```python
z = sy.symbols('z')
y0, y1 = sy.symbols('y0, y1', real=True)
```


```python
den = z*z - z -1
num = z*z
Y = num/sy.factor(den)
sy.factor(den)
```


```python
sy.factor(Y)
```


```python
sy.apart(Y)
```


```python
sy.apart( z/den)
```


```python
p1 = (1 + sy.sqrt(5))/2
p2 = (1 - sy.sqrt(5))/2
sy.expand((z-p1)*(z-p2))
```


```python
Y = z/( (z-p1)*(z-p2))
Y
```


```python
sy.apart(Y)
```


```python

```

33c414fa2617f457486726e25f65900af6839598
ipynb
Jupyter Notebook
discrete-time-systems/notebooks/Fibonacci.ipynb
kjartan-at-tec/mr2007-computerized-control
16e35f5007f53870eaf344eea1165507505ab4aa
MIT
2020-11-07T05:20:37.000Z
2020-12-22T09:46:13.000Z
discrete-time-systems/notebooks/Fibonacci.ipynb
alfkjartan/control-computarizado
5b9a3ae67602d131adf0b306f3ffce7a4914bf8e
MIT
2020-06-12T20:44:41.000Z
2020-06-12T20:49:00.000Z
discrete-time-systems/notebooks/Fibonacci.ipynb
alfkjartan/control-computarizado
5b9a3ae67602d131adf0b306f3ffce7a4914bf8e
MIT
2019-09-25T20:02:23.000Z
2019-09-25T20:02:23.000Z
Qwen/Qwen-72B
1. YES
2. YES