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Home » $S_n$: number of valid strings of length $n$ ending in 3 - Londonproperty

$S_n$: number of valid strings of length $n$ ending in 3 - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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A virologist is studying the combinations of synthetic DNA sequences w...
To solve this, we first compute the total number of 6-nucleotide seque...
Next, we compute the number of sequences that do **not** contain two c...
We derive a recurrence for \(a_n\):
If the first nucleotide is T, the rest \(n-1\) positions form a valid...
If the first is A, the next must be T (to avoid AA), and then \(n-2\)...
So, \(a_n = a_{n-1} + a_{n-2}\), with base cases:
\(a_1 = 2\) (A, T)

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