# GSoC: SymPy - Week 6 & 7

The second phase of Coding Period has started.

I started this phase working on recurrence submodule under `discrete`

. After having an initial discussion with Kalevi regarding the functionality to be implemented, I did the proof-of-concept for the same on a remote branch.

After the approach was finalized, the implementation was polished before opening the PR. The PR #14816 also included documentation, doctests, and unit tests for the module.

The method `linrec(coeffs, init, n)`

takes coefficients, initial values and point of evaluation for the linear recurrence. Usage for a recurrence like `f(n) = f(n - 7) + f(n - 13) + f(n - 17)`

(having order `17`

) would be:

```
In []: coeffs, init = [0]*17, [1]*17
In []: coeffs[7 - 1] = coeffs[13 - 1] = coeffs[17 - 1] = 1
In []: [linrec(coeffs, init, n) for n in range(40, 50)]
Out[]: [17, 21, 21, 23, 29, 31, 31, 35, 41, 41]
In []: def f(n):
...: if n < 17:
...: return 1
...: return f(n - 7) + f(n - 13) + f(n - 17)
...:
In []: [f(n) for n in range(40, 50)]
Out[]: [17, 21, 21, 23, 29, 31, 31, 35, 41, 41]
```

As suggested by Aaron, it will be good to have a user-facing method that calls `linrec`

internally for performing the computation.

Looking forward to another exciting week.

**Published:**28 June 2018