Fibonacci Number

A Fibonacci Number is a Natural Number from the The Fibonacci Number Sequence.

• See: Arithmetic Sequence.

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References

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Fibonacci_number
  • In mathematics, the Fibonacci numbers are the following sequence of numbers:
    • 0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89, \ldots.
  • The first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two:
    • \begin{align} 0 + 1 &= 1 \\ 1 + 1 &= 2 \\ 1 + 2 &= 3 \\ 2 + 3 &= 5 \\ 3 + 5 &= 8 \\ 5 + 8 &= 13 \\ &\;\vdots \end{align}
  • Some sources omit the initial 0, instead beginning the sequence with two 1s.
  • In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation
    • F_n = F_{n-1} + F_{n-2},\!\,
  • with seed values
    • F_0 = 0 \quad\text{and}\quad F_1 = 1.

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