Fibonacci simplify

Questions
1

Hi

I have this expression of Fibonacci:

2*FIB[-1 + n] + FIB[n];

and I want this as result:

2*FIB[-3 + n]

How can I do?

Thanks

Galasi

2

The function for Fibonacci numbers in Mathematica is called Fibonacci:

I’m not sure how much functions like FullSimplfiy are able to reason about expressions with Fibonacci in them, but the identitiy you wrote doesn’t seem to hold. Compare:

Table[Fibonacci[-1 + n] + Fibonacci[n], {n, 1, 10}]

Table[2*Fibonacci[-3 + n], {n, 1, 10}]
3

you are right

Thanks!