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Home » These 7 Happy Friday Quotes Will Turn Your Weekaround! - Dachbleche24

These 7 Happy Friday Quotes Will Turn Your Weekaround! - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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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)
\(a_2 = 3\) (TT, TA, AT — not AA)
\(a_3 = a_2 + a_1 = 3 + 2 = 5\)
\(a_4 = a_3 + a_2 = 5 + 3 = 8\)
\(a_5 = a_4 + a_3 = 8 + 5 = 13\)
\(a_6 = a_5 + a_4 = 13 + 8 = 21\)

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