Given an $n$ letter string of identical letters, how many $k+2$ letter words can be formed of adjacent letters?
By observing data I came up with n-(1+k), but I'm at a loss for a descent combinatorial explanation.
For example, if I had a 5 letter string and k=1 and I label the letters for clarity: 'abcde' I get 'abc', 'bcd', 'cde'.