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{a(n)} is such a sequence, satisfying,

  1. For all a(i) ∈ {a(n)}, a(i) =1 or -1

  2. Let S(j) = Sum[a(i) , {i ,1, j}], then for all 1<=j<=n ,S(j)>=0.

For a given n , how many a{a(n)} are there?

{a(n)} is such a sequence, satisfying,

  1. For all a(i) ∈ {a(n)}, a(i) =1 or -1

  2. Let S(j) = Sum[a(i) , {i ,1, j}], then for all 1<=j<=n ,S(j)>=0.

For a given n , how many a(n) are there?

{a(n)} is such a sequence, satisfying,

  1. For all a(i) ∈ {a(n)}, a(i) =1 or -1

  2. Let S(j) = Sum[a(i) , {i ,1, j}], then for all 1<=j<=n ,S(j)>=0.

For a given n , how many {a(n)} are there?

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user47870
user47870

A problem of a sequence and its sum

{a(n)} is such a sequence, satisfying,

  1. For all a(i) ∈ {a(n)}, a(i) =1 or -1

  2. Let S(j) = Sum[a(i) , {i ,1, j}], then for all 1<=j<=n ,S(j)>=0.

For a given n , how many a(n) are there?