Question: What is a recursive formula to calculate the sequence a0,...,an, which represents the maximum sum of any collection of non-adjacent entries in the length-i prefix

What is a recursive formula to calculate the sequence a0,...,an, which represents the maximum sum of any collection of non-adjacent entries in the length-i prefix of an array A of length n, for any i in {0,...,n}? The recurrence should be solvable in O(n) time. No justification of the recurrence is required.

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