how many n-length bit strings are there, where '00' occurs exactly two times. ( '000' is perceived as two occurings )
we have to distinguish between different kinds of bit strings:
anything else is not a valid bitstring in our example.
it may has something to do with this: id:A055243 - OEIS Search Results
first formulas for solving this are posted here: MP-Forum: Anzahl der Binärwörter mit genau 2-mal "00" (Matroids Matheplanet) ( german )
this is a homework in our discrete mathematics class, i talked with about 20 people who tried to solve this for the last 4 days, no one did. and i am starting to get depressed myself : /