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I want to calculate the amount of elements in a Merkle tree given the number of leaf elements.

The number of elements at a given level n is equal to number of elements at a level n+1, divided by two and rounded up. The highest level are the leaf elements, and the root of the tree contains only one element.

I can calculate the value recursively without any problem, but I'd like to know if there is any formula that could give the result without recursion.

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