Engineering Mathematics Combinatorics Generating Functions

Let a_n represents the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for a_n?

1

a_n-2 + a_n-1 + 2^n-2

2

a_n-2 + 2a_n-1+ 2^n-2

3

2a_n-2 + a_n-1 + 2^n-2

4

2a_n-2 + 2a_n-1 + 2^n-2

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