I would like to find all possible combinations of a matrix columns, with each column contribute a value, in each itteration of a loop. The matrix size changes in each itteration. For example:
A = [1 2 3
4 5 6
7 8 9].
should produce:
1 2 3
1 2 6
1 5 3 etc.
but should not produce:
1 4 2 for example.

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I need to prove this asimptotic equation. I have already limited the sum on the right by 2^(3n) using Newton’s binomial, but I din’t know how to prove that the sum bounded from below by const*2^(3n). I tried to prove that it is comparable to its complement to Newton’s binomial, but this leads to very complex calculations. I think there must be an idea here that I don’t know. I will be glad if someone has fresh thoughts about this problem.