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Home » Growth factor = \( 1 + 0.25 = 1.25 \) - DNSFLEX

Growth factor = \( 1 + 0.25 = 1.25 \) - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 We use **inclusion-exclusion over forbidden adjacents**, but that becomes intractable due to multiple overlapping cases.

📌 Instead, we use a **constructive counting method** with **placement strategy**.

📌 Let’s consider that we are placing 8 positions, assigning A, C, G with multiplicities 2, 3, 3, such that **no two identical letters are adjacent**.

📌 We proceed in steps:

📌 First, place the most frequent letters: C and G (both appear 3 times). Since no two C’s or G’s can be adjacent, we must ensure they are separated.

📌 But we cannot place all three C’s without adjacency unless separated by at least one non-C.

📌 Similarly for G.

📌 A powerful method is to **first arrange the non-C letters**, then insert C’s in safe positions, and similarly for G’s — but since both C and G have 3 copies and adjacency restrictions, and overlap is possible, we need a more systematic way.

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