Fungrim home page

Fungrim entry: b8ed8f

Fn=12n1k=0(n1)/25k(n2k+1)F_{n} = \frac{1}{{2}^{n - 1}} \sum_{k=0}^{\left\lfloor \left( n - 1 \right) / 2 \right\rfloor} {5}^{k} {n \choose 2 k + 1}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
TeX:
F_{n} = \frac{1}{{2}^{n - 1}} \sum_{k=0}^{\left\lfloor \left( n - 1 \right) / 2 \right\rfloor} {5}^{k} {n \choose 2 k + 1}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
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("b8ed8f"),
    Formula(Equal(Fibonacci(n), Mul(Div(1, Pow(2, Sub(n, 1))), Sum(Mul(Pow(5, k), Binomial(n, Add(Mul(2, k), 1))), 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