In the post Sum of combinations of n taken k where k is from n to (n/2)+1, it has been explained clearly how to calculate the summation of combinations from n/2 to n. I was wondering if there is any such formula for calculating the summation of odd/even combinations if n is even/odd.
Formula for summation of all possible combinations of n = 2^n
Suppose, if n is odd,
Summation of odd combinations = summation of even combinations = 2^(n-1).
How to calculate the summation of even or odd combinations if n is even? I am trying to come up with some kind of formula but couldn't. Any help would be appreciated.