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Home » Nutze $a_0 = 5$: $5 = A + 3 \Rightarrow A = 2$ - Groen Casting

Nutze $a_0 = 5$: $5 = A + 3 \Rightarrow A = 2$ - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A virologist is studying the combinations of synthetic DNA sequences where two types of nucleotides, A and T, are used. How many 6-nucleotide sequences can be formed where there are exactly two consecutive A's at least once?

📌 To solve this, we first compute the total number of 6-nucleotide sequences using A and T, which is \(2^6 = 64\).

📌 Next, we compute the number of sequences that do **not** contain two consecutive A’s. Let’s denote this count as \(a_n\) for sequences of length \(n\).

📌 We derive a recurrence for \(a_n\):

📌 If the first nucleotide is T, the rest \(n-1\) positions form a valid sequence: \(a_{n-1}\)

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