Fibonacci sequence

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The Fibonacci spiral Page status: evergreen
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The Fibonacci sequence is defined through the recurrence relation $𝐹_{𝑛} = 𝐹_{𝑛 - 1} + 𝐹_{𝑛 - 2}$ . It can also be expressed in closed form:

$𝐹_{𝑛} = ⌊ \frac{1}{\sqrt{5}} 𝜙^{𝑛} ⌉, 𝜙 = \frac{1 + \sqrt{5}}{2}$

The first 8 numbers of the sequence are:

$𝐹_{1}$	$𝐹_{2}$	$𝐹_{3}$	$𝐹_{4}$	$𝐹_{5}$	$𝐹_{6}$	$𝐹_{7}$	$𝐹_{8}$
1	1	2	3	5	8	13	21

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