Call a set of integers "spacy" if it contains no more than one out of any three consecutive integers.  How many subsets of $\{1, 2,
3, \dots, 12\}$, including the empty set, are spacy?
Question:
Call a set of integers "spacy" if it contains no more than one out of any three consecutive integers.  How many subsets of $\{1, 2,
3, \dots, 12\}$, including the empty set, are spacy?
Answer:
Let's think step by step.

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Call a set of integers "spacy" if it contains no more than one out of any three consecutive integers.  How many subsets of $\{1, 2,
3, \dots, 12\}$, including the empty set, are spacy?
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