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Fungrim entry: 5745bd

F2n=Fn+22Fn+122Fn2F_{2 n} = F_{n + 2}^{2} - F_{n + 1}^{2} - 2 F_{n}^{2}
Assumptions:nZn \in \mathbb{Z}
TeX:
F_{2 n} = F_{n + 2}^{2} - F_{n + 1}^{2} - 2 F_{n}^{2}

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("5745bd"),
    Formula(Equal(Fibonacci(Mul(2, n)), Sub(Sub(Pow(Fibonacci(Add(n, 2)), 2), Pow(Fibonacci(Add(n, 1)), 2)), Mul(2, Pow(Fibonacci(n), 2))))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

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2019-08-19 14:38:23.809000 UTC