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Post Closed as "Not suitable for this site" by user44191, Peter Taylor, Daniele Tampieri, Dag Oskar Madsen, Dave Benson
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Gerry Myerson
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Math_deep
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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

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

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

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
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Math_deep
Math_deep
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A permutation and combination problem about the number of connections in a sequence of n numbers

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