OEIS A000279: One fixed point in three-letter multisets

We explore A000279, counting the number of permutations of n copies of three letters (A, B, C) that have exactly one fixed point. We unpack what a fixed point means in a multiset permutation, describe the rapid exponential growth (~(sqrt(3)/π)·8^n), and summarize the exact counting formula and generating function that connect to reduced HIP polynomials and hypergeometric functions. We also discuss why such precise permutation patterns matter in combinatorics and their potential relevance to cryptography and data integrity checks.

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