Non-Splittable Subsets

Probability Level 5

Let $S$ be a set of three integers chosen from $N = \{1,2,\ldots,2012\}$ . We say that $S$ is 4-splittable if there is an $n \in N \setminus S$ such that $S \cup \{n\}$ can be partitioned into 2 sets such that the sum of each set is the same. How many 3-element subsets of $N$ are not 4-splittable?

Details and assumptions

You can refer to Set Notation for the definition of $N \setminus S$ .