Final answer:
The mathematical formula for counting duplicates in a sequence involves comparing each element in the sequence to every other element and counting how many times the same element occurs.
Step-by-step explanation:
The mathematical formula for counting duplicates in a sequence involves comparing each element in the sequence to every other element and counting how many times the same element occurs. Here is a step-by-step process:
Initialize a counter variable to 0.
Start with the first element in the sequence and compare it to all the other elements.
If the element is found elsewhere in the sequence, increment the counter by 1.
Move to the next element in the sequence and repeat steps 2-3 until all elements have been checked.
The value of the counter represents the number of duplicates in the sequence.
For example, consider the sequence [1, 2, 3, 1, 4, 2, 1].
Comparing 1 to the other elements, we find two duplicates.
Comparing 2 to the other elements, we find one duplicate.
Comparing 3 to the other elements, we find no duplicates.
Comparing 4 to the other elements, we find no duplicates.
So in total, there are three duplicates in the sequence.