Chan Black
06/16/2024 · Elementary School
\( n \) désignant un entier naturel non nul, on considère l'ensemble \( E_{n} \) des mots de \( n \) lettres que l'on peut former à l'aide des lettres a, b et c uniquement et ne contenant pas deux lettres consécutives identiques. On note \( F_{n} \) la partie de \( E_{n} \) constituée par les mots qui commencent et se terminent par deux lettres différentes. On pose \( \alpha_{n}=\operatorname{card}\left(E_{n}\right) \) et \( \beta_{n}=\operatorname{card}\left(F_{n}\right) \). 1. Déterminer \( \alpha_{n} \) en fonction de \( n \).
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La formule pour \( \alpha_n \) est \( \alpha_n = 3 \cdot 2^{n-1} \).
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