# Fibonacci numbers (FORTRAN)

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The Fibonacci numbers are the integer sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., in which each item is formed by adding the previous two. The sequence can be defined recursively by

$F(n) = \begin{cases} 0 & n = 0 \\ 1 & n = 1 \\ F(n-1)+F(n-2) & n > 1 \\ \end{cases} .$

Fibonacci number programs that implement this definition directly are often used as introductory examples of recursion. However, many other algorithms for calculating (or making use of) Fibonacci numbers also exist.

##  Implementation

The [fibonacci] numbers in FORTRAN:

<<fib.f90>>=
program main
implicit none
interface
function fib(n)
integer, intent(in) :: n
integer :: fib
end function fib
end interface

print *, fib(10)
end program main

recursive function fib (n)  result (fnum)
integer, intent(in)  :: n
integer :: fnum
if (n<2) then
fnum = n
else
fnum = fib(n-1) + fib(n-2)
endif
end function fib

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