Fungrim home page

Fungrim entry: 9638c1

Fn=k=0n1(nk1k)F_{n} = \sum_{k=0}^{n - 1} {n - k - 1 \choose k}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
F_{n} = \sum_{k=0}^{n - 1} {n - k - 1 \choose k}

n \in \mathbb{Z}_{\ge 0}
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Sumnf(n)\sum_{n} f(n) Sum
Binomial(nk){n \choose k} Binomial coefficient
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(Fibonacci(n), Sum(Binomial(Sub(Sub(n, k), 1), k), For(k, 0, Sub(n, 1))))),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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