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Fungrim entry: d7c89c

Fn=k=0(n1)/2(nk1k)F_{n} = \sum_{k=0}^{\left\lfloor \left( n - 1 \right) / 2 \right\rfloor} {n - k - 1 \choose k}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
F_{n} = \sum_{k=0}^{\left\lfloor \left( n - 1 \right) / 2 \right\rfloor} {n - k - 1 \choose k}

n \in \mathbb{Z}_{\ge 0}
Definitions:
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:
Entry(ID("d7c89c"),
    Formula(Equal(Fibonacci(n), Sum(Binomial(Sub(Sub(n, k), 1), k), For(k, 0, Floor(Div(Sub(n, 1), 2)))))),
    Variables(n),
    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.

2019-10-05 13:11:19.856591 UTC