L3 google onsite Arithmetic sequence question.

Hi everyone, I recently completed my google loop, unfortunatly i was rejected because i bombed the round where i was asked this question, i panicked and managed only a brute force with a couple of hints.

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it from the previous one, the difference is always a constant.

A good arithmetic sequence is an arithmetic sequence with a common difference of either 1 or -1.

For example, [4, 5, 6] is a good arithmetic sequence. Any sequence that has only one element is a good arithmetic sequence.

For example, [4] is a good arithmetic sequence.

Given an integer array nums, return the sum of the sums of each subarray that is a good arithmetic sequence.

Example:

Given nums = [7, 4, 5, 6, 5]. Each of the following subarrays is a good arithmetic sequence:

• [7], [4], [5], [6], [5],
• [4, 5], [5, 6], [6, 5],
• [4, 5, 6]

The sums of these subarrays are:

• 7, 4, 5, 6, 5,
• 4 + 5 = 9, 5 + 6 = 11, 6 + 5 = 11,
• 4 + 5 + 6 = 15

Thus, the answer is the sum of all the sums above, which is:

7 + 4 + 5 + 6 + 5 + 9 + 11 + 11 + 15 = 73.

Now I know that we can find the start and end of each sequence and calculate how many segments each number appears in. Unfortunatly I didn't know that pattern and math formula before this interview...