How to write the Fibonacci Sequence?

I had originally coded the program wrongly. Instead of returning the Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 should = only those numbers between 1 & 20), I have written for the program to display all Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 displays = First 20 Fibonacci numbers). I thought I had a sure-fire code. I also do not see why this is happening.