I am trying to solve some basic question in computer science although the problem is that I can't figure out how to calculate the combinatorial equation to solve my problem.
Consider a row with with $x$ chairs. in first place (from left to right) should always be a person, next should be maximum 4 empty spaces and then another person and so on. It is possible for the row to have only one place which will be occupied or a place and two, three or four empty spaces and so on. Example for valid rows:
p - - - - p - - - - p - -
p - - - - p -
p - -
p
Example of invalid rows:
- p - - -
p - - - - -
p - p
p - - p
p - - - p
How can I build an equation to calculate the number of occupied chairs?
EDIT: the following table:
total not-empty chairs
1 1
2 1
3 1
4 1
5 1
6 2
7 2
8 2
9 2
10 2
11 3
12 3
It is $\lceil \frac{x}{5} \rceil$ - this means $\frac{x}{5}$ rounded up to the closest integer.