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michigan is bracing for up to a foot more snow - ClickBalance

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 Base cases:

📌 $ n = 1 $: sequences: "3", "7" → both valid → $ a_1 = 2 $

📌 $ n = 2 $: "37", "73", "77", "33" → exclude "33" → 3 valid → $ a_2 = 3 $

📌 $ a_4 = 5 + 3 = 8 $

📌 $ a_5 = 8 + 5 = 13 $

📌 $ a_6 = 13 + 8 = 21 $

📌 So 21 sequences with no two consecutive 3s.

📌 Total sequences: $ 2^6 = 64 $

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