# Suppose that a recursive routine were invoked to calculate F(4). How many times would a recursive call of F(1) occur?

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Expert Answers

lfryerda | Certified Educator

Although you haven't said so explicitly, it seems as though you are talking about Fibonacci sequences, since the usual notation for that in Mathematics/Computer Science classes is F(n), and the routines are recursive. The Fibonacci sequence is defined as:

`F(n)=F(n-1)+F(n-2)` , where `F(2)=1` and `F(1)=1` .

which means that

`F(4)=F(3)+F(2)`

And we can see that the recursive calls continue as

`F(3)=F(2)+F(1)`

**This means that the call of `F(1)=1` is called only once.**

Student Comments

winnie7 | Student

F(4) = F(3) + F(2)

= F(2) + F(1) + F(1) + F(0)

= F(1) + F(0)+ F(1) + F(1) + F(0)

= 3F(1) + 2F(0)

So, it gets call 3 times.