Shell Script to Generate Fibonacci Series

  By definition in mathematics, the Fibonacci Numbers are the numbers
in the below sequence:
0,1,1,2,3,5,8,13,21,34,55,89,144, ......
  By definition, the first two Fibonacci numbers are 0 and 1, and each
subsequent number is the sum of the previous two. Some sources omit
the initial 0, instead beginning the sequence with two 1s.
  In mathematical terms, the sequence Fn of Fibonacci numbers is defi-
ned by the recurrence relation
    Fn = Fn-1 + Fn-2,
with seed values
   F0 = 0 and F1 = 1.

Iterative Method: 
#!/bin/bash#!/bin/bash
# SCRIPT:  fibo_iterative.sh
# USAGE:   fibo_iterative.sh [Number]
# PURPOSE: Generate Fibonacci sequence.
#                         \\\\ ////
#                         \\ - - //
#                            @ @
#                    ---oOOo-( )-oOOo---
#
#####################################################################
#                     Script Starts Here                            #
#####################################################################

if [ $# -eq 1 ]
then
    Num=$1
else
    echo -n "Enter a Number :"
    read Num
fi

f1=0
f2=1

echo "The Fibonacci sequence for the number $Num is : "

for (( i=0;i<=Num;i++ ))
do
     echo -n "$f1 "
     fn=$((f1+f2))
     f1=$f2
     f2=$fn
done

echo

OUTPUT:
# sh fibo_iterative.sh 18
The Fibonacci sequence for the number 18 is : 
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 
# sh fibo_iterative.sh
Enter a Number :20
The Fibonacci sequence for the number 20 is : 
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 

Recursive Method:
#!/bin/bash
# SCRIPT:  fibo_recursive.sh
# USAGE:   fibo_recursive.sh [Number]
# PURPOSE: Generate Fibonacci sequence.
#                         \\\\ ////
#                         \\ - - //
#                            @ @
#                    ---oOOo-( )-oOOo---
#
#####################################################################
#                      Arguments Checking                           #
#####################################################################

if [ $# -eq 1 ]
then
    Num=$1
else
    echo -n "Enter a Number : "
    read Num
fi

#####################################################################
#                      Define Functions Here                        #
#####################################################################

Fibonacci()
{

case $1 in
 0|1) printf "$1 " ;;
 *) echo -n "$(( $(Fibonacci $(($1-2)))+$(Fibonacci $(($1-1))) )) ";;
esac

#$(( )) construct is used instead of expr command for doing addition.
#$( ) constrict is used instead of back ticks.

}

#####################################################################
#                      Main Script Starts Here                      #
#####################################################################

echo "The Fibonacci sequence for the number $Num is : "

for (( i=0; i<=$Num; i++ ))
do
  Fibonacci $i                     #Calling function Fibonacci
done

echo

OUTPUT:
# sh fibo_recursive.sh 
Enter a Number : 11
The Fibonacci sequence for the number 11 is : 
0 1 1 2 3 5 8 13 21 34 55 89 
# sh fibo_recursive.sh 13
The Fibonacci sequence for the number 13 is : 
0 1 1 2 3 5 8 13 21 34 55 89 144 233 

Be aware that recursion is resource-intensive and executes slowly,
and is therefore generally not appropriate to use in a script.

[root@localhost shell]# time ./fibo_iterative.sh 15
The Fibonacci sequence for the number 15 is :
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610

real    0m0.008s
user    0m0.008s
sys     0m0.000s
[root@localhost shell]# time ./fibo_recursive.sh 15
The Fibonacci sequence for the number 15 is :
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610

real    0m7.875s
user    0m0.908s
sys     0m5.188s

Too many levels of recursion may crash a script with a segfault.