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This is in simplest form. - GetMeFoodie

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 But we must subtract or eliminate sequences where **identical nucleotides are adjacent**, particularly the two A’s and the three C’s or three G’s.

📌 However, due to the complexity of inclusion-exclusion over multiple repeated elements and spatial constraints, we instead model this using **inclusion with arrangement constraints** — specifically, placing the letters so that no two identical ones are adjacent.

📌 A better approach is constructive: build the sequence step-by-step, placing the letters while avoiding adjacent duplicates.

📌 But because we have repeated letters and exact counts, we use a **recursive or combinatorial placement strategy** with the principle of **arrangements with no adjacent duplicates** for multiset permutations.

📌 However, due to the complexity and size, we apply a known combinatorial method: **counting valid permutations with forbidden adjacency** using inclusion-exclusion or generating functions — but a more efficient way is to use **placement algorithms**.

📌 Alternatively, we proceed by **constructing valid sequences** using dynamic programming or recursive counting, but for Olympiad-style reasoning, we can use the **principle of arranging with separation**.

📌 But here’s a better and feasible approach:

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

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