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Let $T_n$ be the set

$$T_n = \left\{(a_1,\dots,a_n) \in \{0,1\}^n \middle\vert \text{ no two 0s can appear in two adjacent components}\right\}. $$

Let $t_n = \#T_n$ be the cardinality of $T_n$.

How would I go about finding $t_1, t_2, t_3$, and their their relationship to each other?

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    There isn't really anything to do other than write down what T1, T2, and T3 are. What exactly are you stuck on?2011-04-11
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    I agree with Zev. What have you tried so far? For example, what problem are having with finding the cardinality of $T1$? Also, for future reference, please do not post in the imperative mode. Please word your post as a question.2011-04-11
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    Can you please explain your answer. I do not understand how t1= 2? Shouldn't it equal 1.2011-04-11
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    $T_1=\{(0),(1)\}$.2011-04-11

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