I am not sure that I understand what you have written.

Here is a stab at an answer.

Consider the set of digits: .

I can select four of those with no two consecutive in ways.

We can select up to five digits with no consecutive digits.

If you had 15 items you can select up to 8 with no two consecutive.

For n items you can select up to with no two consecutive. That is the ceiling function.

The number of ways of selecting k items is .

If that is not what mean, please try to make is clear what you do mean.