Base:

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• Total sequences: \(2^9 = 512\)
• Let \(b_n\) be the number of binary sequences of length \(n\) with no two consecutive C’s (C = communal).
• Same recurrence: \(b_n = b_{n-1} + b_{n-2}\)
• \(b_1 = 2\) (C, I)
• \(b_2 = 3\) (II, IC, CI — not CC)
• \(b_3 = b_2 + b_1 = 3 + 2 = 5\)

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