The inner loop of the cubic maximum subsequence sum, Basic Computer Science

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The inner loop of the cubic maximum subsequence sum

The inner loop of the cubic maximum subsequence sum algorithm performs N(N+1)(N+2)/6 iterations of the innermost code. The quadratic version performs N(N + 1)/2 iterations. The linear version performs N iterations. What pattern is evident? Can you give a combinatoric explanation of this phenomenon?

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Basic Computer Science: The inner loop of the cubic maximum subsequence sum

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Basic Computer Science: The inner loop of the cubic maximum subsequence sum

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