There are a total of 3 ways to loop 4 points. The graphics below shows all possible ways to loop 4 points. For each permutation, there are n permutations that is itself shifted, counting itself. You may look up N.J.A. Sloane's on-line Integer Sequence Encyclopedia to see interesting facts about this sequence. To enumerate all all possible lists, we can start with a complete permutations and delete shift and reversal equivalents.
Direct method is also possible.
Here is an insight to such method. Following that we will work it out slowly. Its second element is smaller than the last element. Choose an unordered pair of numbers 2 to n. Take any permutation of the remaining n-3 numbers.