Fungrim entry: 35956b

F_{2 n} = F_{n + 1}^{2} - F_{n - 1}^{2}

Assumptions:

n \in \mathbb{Z}

TeX:

F_{2 n} = F_{n + 1}^{2} - F_{n - 1}^{2}

n \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`Fibonacci`	$F_{n}$	Fibonacci number
`Pow`	${a}^{b}$	Power
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("35956b"),
    Formula(Equal(Fibonacci(Mul(2, n)), Sub(Pow(Fibonacci(Add(n, 1)), 2), Pow(Fibonacci(Sub(n, 1)), 2)))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

Topics using this entry

Fibonacci numbers

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC