GeoGebra examples for recursive functions:

"First Order": Suppose $f : N \rightarrow N $ with $f(0)=a$ and $f(n+1)=g(n,f(n))$, where $n$ is a natural number

"Second Order": Suppose $f : N \rightarrow N $ with $f(0)=a$, $f(1)=b$ and $f(n+2)=g(n+2,f(n), f(n+1))$, where $n$ is a natural number

You can change the recursive function from $f(n+2) = g(n+2,f(n),f(n+1))$ by changing the definition of $g$, as well as by changing the initial values, $f(0) = a$ and $f(1) = b$.