Geometric Sequence Triplets

A geometric sequence triplet is a sequence of three numbers where each successive number is obtained by multiplying the preceding number by a constant called the common ratio.

Let's examine three triplets to understand how this works:

• (1, 2, 4): This is a geometric sequence with a ratio of 2 (i.e., [1, 1⋅2 = 2, 2⋅2 = 4]).
• (5, 15, 45): This is a geometric sequence with a ratio of 3 (i.e., [5, 5⋅3 = 15, 15⋅3 = 45]).
• (2, 3, 4): Not a geometric sequence.

Given an array of integers and a common ratio r, find all triplets of indexes (i, j, k) that follow a geometric sequence for i < j < k. It's possible to encounter duplicate triplets in the array.

Example:

Input: nums = [2, 1, 2, 4, 8, 8], r = 2
Output: 5

Explanation:

• Triplet [2, 4, 8] occurs at indexes (0, 3, 4), (0, 3, 5), (2, 3, 4), (2, 3, 5).
• Triplet [1, 2, 4] occurs at indexes (1, 2, 3).