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Fungrim entry: d7c89c

Fn=∑k=0⌊(n−1)/2⌋(n−k−1k)F_{n} = \sum_{k=0}^{\left\lfloor \left( n - 1 \right) / 2 \right\rfloor} {n - k - 1 \choose k}
Assumptions:n∈Z≥0n \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
Sum∑nf(n)\sum_{n} f(n) Sum
Binomial(nk){n \choose k} Binomial coefficient
ZZGreaterEqualZ≥n\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

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2021-03-15 19:12:00.328586 UTC