Even odd and difference property(s) of fibonacci numbers

A In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones:[1][2] 1,1,2,3,5,8,13,21,34 ................(1) Often, especially in modern usage, the sequence is extended by one more initial term: 0,1,1,2,3,5,8,13,21,34,...........[3] (2) From the plan mathematical observation, the Fibonacci series has even-odd and difference property. The even-odd property means that the series first number is always even and further two numbers are always odd when we consider (2).But if we consider (1) the then first two numbers are always odd and next number is always even. Also, the difference property means that by considering (2), when we subtract (n+1) number with nth number the preceding number comes. The astounding fact is that it generates the total Fibonacci series again. Also, I have implemented the above properties and generated the Fibonacci series using c programming language.