For calculating the index of coincidence for each sequence

Question

I was learning about the finding the key length reading the following web site... http://practicalcryptography.com/cryptanalysis/stochastic-searching/cryptanalysis-vigenere-cipher/

and I really don't understand some part of the example shown in the web. They assume the key length is 2 and extract the two sequence 1,3,5,7.... and 2,4,6,8... and from these two sequences they calculate the I.C.

I wasn't sure how they calculate the I.C. for each sequence. Do they find the frequency count of each letter from a to z, and calculate the I.C using the following formula?

Answer 1

As explained on the link you posted, the Vigenere cipher with a key on length $n$ encrypts every $n$-th symbol with the same key under the Caesar cipher. So to calculate the IC you should take all the $n$ sub-sequences separately: $\{1, 1+n, \dots, 1+kn, \dots\}$, $\{2, 2+n, \dots, 2+kn, \dots\}$ and so on and compute the IC for every sub-sequence.