### Input area

Auto-fill examples:

Manual input:- On the first line write the coefficients of the recurrence relation, separated by spaces.
- On the second line write an equal number of space-separated initial values.
- The LRS must be simple, non-degenerate, and not the zero LRS.
- The tool will output all zeros (at both positive and negative indices), along with a completeness certificate.

```
a
```_{1} a_{2} ... a_{k}

u_{0} u_{1} ... u_{k-1}

where:```
u
```_{n+k} = a_{1}·u_{n+k-1} + a_{2}·u_{n+k-2} + ... + a_{k}·u_{n}

Auto-fill examples:

Manual input: