Question:(adsbygoogle = window.adsbygoogle || []).push({});

"Find a recurrence relation and initial conditions for the sequence {a sub n} if a sub n is the number of bit strings of length n that contain three consecutive 0's."

So here's what I have so far...

n > 3

n = 4, 1000, 0001

n = 5, 10000, 00001, 00010, 01000, 10001

n = 6, 100000, 000001, 010000, 000010, 001000, 00100, 111000, 000111, 110001, 100011, 110000, 000011, 100001, 101000, 000101, 100010, 010001, ... I might have missed a few...

Anyways here's what I see... As n increases the number of bit strings increases (almost exponentially), and the maximum number of 1's in the string is n-3. In n-6, you have 3x1's.

That's all I have so far... And I don't know where else to go from here. So I would like some help with this.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: [Discrete Math] Recurrence Relations

**Physics Forums | Science Articles, Homework Help, Discussion**