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Fungrim entry: 8a548e

(1110)n=(Fn+1FnFnFn1){\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}}^{n} = \begin{pmatrix} F_{n + 1} & F_{n} \\ F_{n} & F_{n - 1} \end{pmatrix}
Assumptions:nZn \in \mathbb{Z}
TeX:
{\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}}^{n} = \begin{pmatrix} F_{n + 1} & F_{n} \\ F_{n} & F_{n - 1} \end{pmatrix}

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
Matrix2x2(abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix} Two by two matrix
FibonacciFnF_{n} Fibonacci number
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("8a548e"),
    Formula(Equal(Pow(Matrix2x2(1, 1, 1, 0), n), Matrix2x2(Fibonacci(Add(n, 1)), Fibonacci(n), Fibonacci(n), Fibonacci(Sub(n, 1))))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

Topics using this entry

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

2019-08-19 14:38:23.809000 UTC