Fungrim home page

Fungrim entry: 5cb57e

Fn=Fm+1Fnm+FmFnm1F_{n} = F_{m + 1} F_{n - m} + F_{m} F_{n - m - 1}
Assumptions:mZ  and  nZm \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
F_{n} = F_{m + 1} F_{n - m} + F_{m} F_{n - m - 1}

m \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(Fibonacci(n), Add(Mul(Fibonacci(Add(m, 1)), Fibonacci(Sub(n, m))), Mul(Fibonacci(m), Fibonacci(Sub(Sub(n, m), 1)))))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZ), 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.

2021-03-15 19:12:00.328586 UTC