fibonacci sequence - Wolfram|Alpha

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Input interpretation

Fibonacci sequence (A000045)

Alternate names

golden sequence | Lamé's sequence

Notation

F_n

Sequence description

sequence in which each term is the sum of the two previous terms with F_0 = 0, F_1 = 1, F_n = F_(n - 1) + F_(n - 2)

Sequence terms

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, ...

More information »

Formula

a_n = (ϕ^n - (-ϕ)^(-n))/sqrt(5)

Recurrence relation

a_0 = 0

a_1 = 1

a_n = a_(n - 2) + a_(n - 1)

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