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    I don't understand what do you mean contribution. Can you elaborate more?

    "Now, count contributions of each number in the 'pieces'. For example, in pair (1,3), 1 and 3 contribute twice. in pair (1,3,6), 1,2and3 contribute thrice."

    In addition, when n is large, wouldn't the second term of the artithmetic grow bigger than the first term and therefore yield negative result?

    | 2^n-1 | p+2^(y) - 2^0 | p+2^(y-1) - 2^1 | p+2^(y-2) - 2^2|...