Given a integer n, we can generate a sequence [0,1,2,3,4,..., 2^n-1], then we separate it to two sequence according to their index position which is odd or even. We repeat this action until the number of sequence equal 2.

for example:

n = 3;

v = [0, 1, 2, 3, 4, 5 , 6, 7]

step 1:

O = [0, 2, 4, 6]

E = [1, 3, 5, 7]

so v1 = {[0, 2, 4, 6], [1, 3, 5, 7]}

step 2:

for every element of this cell, wo separate, we can get

v2 = {[0, 4], [2, 6], [1, 5], [3, 7]}

this is the solution, because the number of every element is two.

have fun!