There is a sequence of n numbers as 1,2,3,...,n How many combinations of the connections between two numbers in the sequence without overlaping?

Take a sequence 1,2,3,4,5,6,7,8,9,10 for example:  
combination 1: (1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9),(9,10) is allowable
combination 2: (1,2),(3,4),(5,6),(7,8),(9,10) is allowable
combination 3: (1,3),(3,5),(6,8) is allowable
combination 4: (2,6),(7,8) is allowable
combination 5: (2,5),(4,6) is unallowable, because the overlaping exsits