Ononot — Let Sn be the number of subsets of \{1, 2, \dots, n\} that d

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Let $S_n$ be the number of subsets of $\{1, 2, \dots, n\}$ that do not contain any two consecutive integers. Which of the following describes the recurrence and initial conditions for $S_n$ for $n \geq 1$ (with $S_0 = 1$ )?