Thread: advanced counting: bit strings with 2x '00'

how many n-length bit strings are there, where '00' occurs exactly two times. ( '000' is perceived as two occurings )

my try:

we have to distinguish between different kinds of bit strings:

1. ..00..00..
2. ..000...

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 : /

Originally Posted by dayscott

how many n-length bit strings are there, where '00' occurs exactly 2x times. ( '000' is perceived as two occurings )
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 : /

I can see why no one has solved it. It is meaningless as written.
What does 2x mean? What is x?
It may mean that the pattern "00" appears an even number of times??
Is that the exact statement?
If not post the exact problem as it is written,

i am sorry - i fixed the excercise, it should be understandable now