Count of subarrays forming an AP

First clarify the expected minimum length: many versions count arithmetic subarrays of length at least three, while a different convention may include pairs. For the common length-three version, scan adjacent differences. Keep run, the number of additional valid arithmetic subarrays ending at the current index. If a[i]-a[i-1] equals the previous difference, increment run and add it to the answer; otherwise reset run to zero. For a constant-difference block of length L, this accumulates 1 + 2 + ... + (L-2), exactly the count of contiguous subarrays of length at least three. State that the invariant is: before adding, run represents valid AP subarrays ending at i-1 that can be extended by the current element. Use a wide numeric type if n can be large. Handle arrays shorter than three, equal values with difference zero, negatives, and difference overflow. The scan is O(n) time and O(1) space.