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The counts of compositions of n under different restrictions generate a variety of integer sequences. Here we examine seventeen different types of restricted compositions whose counts correspond to the Fibonacci numbers: three classical, two due to Jörg Arndt, one from Checa and Ramírez, and eleven that we believe are newly documented here. We also consider two generalizations of some of these restricted compositions.
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Hopkins et al. (2026) studied this question.
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