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"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.

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# [Discrete Math] Recurrence Relations

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