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behold i am doing a new thing - AIKO, infinite ways to autonomy.

📅 May 4, 2026 👤 scraface

May 04, 2026

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📝 Recent Posts

This is a classic problem: number of binary strings of length \(n\) wi...
Standard recurrence:
Let \(a_n\) = number of such strings of length \(n\).
\(a_1 = 2\) (0, 1),
\(a_2 = 3\) (00, 01, 10, not 11)
Wait — earlier we used \(\binom{n-k+1}{k}\), but for \(n=5\):
List all valid strings (no "11"):
Size 0: 1 (empty)
Size 1: 0, 1 → 2
Size 2: 00, 01, 10 → 3

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