Hosoya's triangle

{{Short description|Triangular arrangement of numbers based on the Fibonacci numbers}}

Hosoya's triangle or the Hosoya triangle (originally Fibonacci triangle; {{OEIS2C|id=A058071}}) is a triangular arrangement of numbers (like Pascal's triangle) based on the Fibonacci numbers. Each number is the sum of the two numbers above in either the left diagonal or the right diagonal.{{Cite journal |last=Hosoya |first=Haruo |author-link=Haruo Hosoya |date=1976 |title=Fibonacci Triangle |journal=The Fibonacci Quarterly |volume=14 |issue=2 |pages=173–178|doi=10.1080/00150517.1976.12430575 }}

{{Image frame|caption=A diagram showing the first 12 rows of Hosoya's triangle

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$$

\begin{array}{c}

1 \\

1 \quad 1 \\

2 \quad 1 \quad 2 \\

3 \quad 2 \quad 2 \quad 3 \\

5 \quad 3 \quad 4 \quad 3 \quad 5 \\

8 \quad 5 \quad 6 \quad 6 \quad 5 \quad 8 \\

13 \quad 8 \quad 10 \quad 9 \quad 10 \quad 8 \quad 13 \\

21 \quad 13 \quad 16 \quad 15 \quad 15 \quad 16 \quad 13 \quad 21 \\

34 \quad 21 \quad 26 \quad 24 \quad 25 \quad 24 \quad 26 \quad 21 \quad 34 \\

55 \quad 34 \quad 42 \quad 39 \quad 40 \quad 40 \quad 39 \quad 42 \quad 34 \quad 55 \\

89 \quad 55 \quad 68 \quad 63 \quad 65 \quad 64 \quad 65 \quad 63 \quad 68 \quad 55 \quad 89 \\

144 \quad 89 \quad 110 \quad 102 \quad 105 \quad 104 \quad 104 \quad 105 \quad 102 \quad 110 \quad 89 \quad 144 \\

\end{array}

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