2
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Show that $f_{n-1} + L_n = 2f_{n}$.

So we need to find a $2$ to $1$ correspondence.

Set 1: Tilings an $n$-board.

Set 2: Tiling of an $n-1$-board or tiling of an $n$-bracelet.

So we need to decompose a tiling of an $n$-board to a tiling of an $n-1$-board or a tiling of an $n-1$-bracelet?

Source: Proofs that Really Count by Art Benjamin and Jennifer Quinn

  • 1
    Clarifications: What is a $n$-board? Is it a $n \times 2$ board? What are your tiling pieces? Are they dominoes and $2 \times 2$ squares? What is $f_n$? The number of ways to tile a $n \times 2$ board with dominoes and squares? A previous question you asked leads me to believe this. These clarifications may allow more people to answer your question.2010-12-27
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    The $f_n$ are Fibonacci numbers, or something else?2010-12-27
  • 0
    @J.M.: yes $f_{n} = F_{n+1}$.2010-12-27
  • 1
    Why not the rest of the questions? What is an $n$-board? What are your tiling pieces?2010-12-27

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