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Fungrim entry: 050fdb

Fn=⌊φn5+12⌋F_{n} = \left\lfloor \frac{{\varphi}^{n}}{\sqrt{5}} + \frac{1}{2} \right\rfloor
Assumptions:n∈Z≥0n \in \mathbb{Z}_{\ge 0}
TeX:
F_{n} = \left\lfloor \frac{{\varphi}^{n}}{\sqrt{5}} + \frac{1}{2} \right\rfloor

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
GoldenRatioφ\varphi The golden ratio (1.618...)
Sqrtz\sqrt{z} Principal square root
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("050fdb"),
    Formula(Equal(Fibonacci(n), Floor(Add(Div(Pow(GoldenRatio, n), Sqrt(5)), Div(1, 2))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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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