Lessons from Arithmetic Slices

Three points:

$1.$ Recognizing arithmetic sequences lets you apply closed-form counting formulas instead of nested loops.

$2.$ The number of subarrays of length at least $3$ in a sequence of length $k$ is $\frac{(k-2)(k-1)}{2}$, derived from summing $1 + 2 + ... + (k-2)$.

$3.$ Track state (current sequence length and difference) to avoid recomputing from scratch at each position.