(d) Given that n is even, how many 00-free bitstring of length n where n is even have exactly (끌 + 1) 1's? (끌 + 2) 1's? (e) Generalizing on your answer from (d), explain why the following is true for an even value n: El 2i + 1 +1' = fn+2 i=0 where fn+2 is the (n + 2)th Fibonnacci number.

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Chapter2: Second-order Linear Odes
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(d) Given that n is even, how many 00-free bitstring of length n where n is even have
exactly (+ 1) 1's? (플 + 2) 1's?
(e) Generalizing on your answer from (d), explain why the following is true for an even
value n:
Σ
i+ 플 + 1
fn+2
2i + 1
i=0
where fn+2 is the (n + 2)th Fibonnacci number.
Transcribed Image Text:(d) Given that n is even, how many 00-free bitstring of length n where n is even have exactly (+ 1) 1's? (플 + 2) 1's? (e) Generalizing on your answer from (d), explain why the following is true for an even value n: Σ i+ 플 + 1 fn+2 2i + 1 i=0 where fn+2 is the (n + 2)th Fibonnacci number.
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