Let n be a positive integer. Find the number of sequences x1,x2,…x2n−1,x2n, where xi∈{−1,1} for each i, satisfying the following condition: for any integer k and m such that 1≤k≤m≤n then the following inequality holds i=2k−1∑2mxi≤ 2 inequalitiescombinatorics proposedcombinatorics