Arithmetic Slices - Implementation

Here's the solution:

function numberOfArithmeticSlices(nums)
    n := length of nums
    if n < 3 then
        return 0
    count := 0
    length := 2  // current arithmetic sequence length
    for i from 2 to n - 1
        if nums[i] - nums[i - 1] = nums[i - 1] - nums[i - 2] then
            length := length + 1
        else
            if length ≥ 3 then
                k := length - 2
                count := count + (k × (k + 1)) / 2
            length := 2
    if length ≥ 3 then
        k := length - 2
        count := count + (k × (k + 1)) / 2
    return count

The formula $(k \times (k + 1)) / 2$ counts slices for a sequence of length $length = k + 2$. This runs in $O(n)$ time.