Find a recurrence relation for the number of binary strings of length
n
that contain three consecutive 0 's. a)
a_(n)=a_(n-1)+2a_(n-2)+2a_(n-3)
; b)
a_(n)=2a_(n-1)+2^(n-3)
; c)
a_(n)=a_(n-1)+a_(n-2)+a_(n-3)
; d)
a_(n)=a_(n-1)+a_(n-2)+a_(n-3)+2^(n-3)
; e)
a_(n)=a_(n-1)+a_(n-2)+2^(n-3)
.

Question

Find a recurrence relation for the number of binary strings of length

n

that contain three consecutive 0 's. a)

a_(n)=a_(n-1)+2a_(n-2)+2a_(n-3)

; b)

a_(n)=2a_(n-1)+2^(n-3)

; c)

a_(n)=a_(n-1)+a_(n-2)+a_(n-3)

; d)

a_(n)=a_(n-1)+a_(n-2)+a_(n-3)+2^(n-3)

; e)

a_(n)=a_(n-1)+a_(n-2)+2^(n-3)

.

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