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Home » Gold Zeus Just Blazed Online—Get Ready for a Gold-Rush Shocking You! - Dachbleche24

Gold Zeus Just Blazed Online—Get Ready for a Gold-Rush Shocking You! - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Now count the number of such numbers that do **not** contain two consecutive 3s. Let $a_n$ be the number of valid sequences of length $n$ with no two consecutive 3s, where each digit is 3 or 4.

📌 We define a recurrence:

📌 If the first digit is 4, the remaining $n-1$ digits form a valid sequence: $a_{n-1}$

📌 If the first digit is 3, the next must be 4, and the rest $n-2$ digits form a valid sequence: $a_{n-2}$

📌 a_1 = 2 \quad (\text{3 or 4}),\quad a_2 = 3 \quad (\text{34, 43, 44})

📌 Compute up to $a_8$:

📌 a_3 = a_2 + a_1 = 3 + 2 = 5 \\

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